{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T13:52:25Z","timestamp":1773237145398,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,1,15]],"date-time":"2016-01-15T00:00:00Z","timestamp":1452816000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta. Math. Sin.-English Ser."],"published-print":{"date-parts":[[2016,2]]},"DOI":"10.1007\/s10114-016-5104-4","type":"journal-article","created":{"date-parts":[[2016,1,7]],"date-time":"2016-01-07T23:13:55Z","timestamp":1452208435000},"page":"137-152","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some specific unboundedness property in smoothness Morrey spaces. The non-existence of growth envelopes in the subcritical case"],"prefix":"10.1007","volume":"32","author":[{"given":"Dorothee D.","family":"Haroske","sequence":"first","affiliation":[]},{"given":"Susana D.","family":"Moura","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,1,15]]},"reference":[{"key":"5104_CR1","volume-title":"Interpolation of Operators","author":"C. Bennett","year":"1988","unstructured":"Bennett, C., Sharpley, R.: Interpolation of Operators, Academic Press, Boston, 1988"},{"key":"5104_CR2","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/S0022-1236(03)00181-2","volume":"208","author":"G. Dafni","year":"2004","unstructured":"Dafni, G., Xiao, J.: Some new tent spaces and duality theorems for fractional Carleson measures and Q \u03b1(Rn). J. Funct. Anal., 208, 377\u2013422 (2004)","journal-title":"J. Funct. Anal."},{"key":"5104_CR3","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511662201","volume-title":"Function Spaces, Entropy Numbers, Differential Operators","author":"D. E. Edmunds","year":"1996","unstructured":"Edmunds, D. E., Triebel, H.: Function Spaces, Entropy Numbers, Differential Operators, Cambridge Univ. Press, Cambridge, 1996"},{"key":"5104_CR4","first-page":"1","volume":"66","author":"A. El Baraka","year":"2002","unstructured":"El Baraka, A.: An embedding theorem for Campanato spaces. Electron. J. Differential Equations, 66, 1\u201317 (2002)","journal-title":"Electron. J. Differential Equations"},{"key":"5104_CR5","volume-title":"Electron. J. Differ. Equ. Conf. 9","author":"A. El Baraka","year":"2002","unstructured":"El Baraka, A.: Function spaces of BMO and Campanato type, Proc. of the 2002 Fez Conference on Partial Differential Equations, 109\u2013115 (electronic), Electron. J. Differ. Equ. Conf. 9, Southwest Texas State Univ., San Marcos, TX, 2002"},{"key":"5104_CR6","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1155\/2006\/921520","volume":"4","author":"A. El Baraka","year":"2006","unstructured":"El Baraka, A.: Littlewood\u2013Paley characterization for Campanato spaces. J. Funct. Spaces Appl., 4, 193\u2013220 (2006)","journal-title":"J. Funct. Spaces Appl."},{"key":"5104_CR7","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1512\/iumj.2000.49.1732","volume":"49","author":"M. Ess\u00e9n","year":"2000","unstructured":"Ess\u00e9n, M., Janson, S., Peng, L., et al.: Q spaces of several real variables. Indiana Univ. Math. J., 49, 575\u2013615 (2000)","journal-title":"Indiana Univ. Math. J."},{"key":"5104_CR8","volume-title":"Limiting Embeddings, Entropy Numbers and Envelopes in Function Spaces, Habilitationsschrift","author":"D. D. Haroske","year":"2002","unstructured":"Haroske, D. D.: Limiting Embeddings, Entropy Numbers and Envelopes in Function Spaces, Habilitationsschrift, Friedrich-Schiller-Universit\u00e4t Jena, Germany, 2002"},{"key":"5104_CR9","volume-title":"Envelopes and Sharp Embeddings of Function Spaces, volume 437 of Chapman & Hall\/CRC Research Notes in Mathematics","author":"D. D. Haroske","year":"2007","unstructured":"Haroske, D. D.: Envelopes and Sharp Embeddings of Function Spaces, volume 437 of Chapman & Hall\/CRC Research Notes in Mathematics, Chapman & Hall\/CRC, Boca Raton, FL, 2007"},{"key":"5104_CR10","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1007\/s10114-012-1119-7","volume":"28","author":"D. D. Haroske","year":"2012","unstructured":"Haroske, D. D., Skrzypczak, L.: Continuous embeddings of Besov\u2013Morrey function spaces. Acta Math. Sin., Engl. Ser., 28, 1307\u20131328 (2012)","journal-title":"Acta Math. Sin., Engl. Ser."},{"key":"5104_CR11","doi-asserted-by":"crossref","first-page":"119","DOI":"10.4064\/sm218-2-2","volume":"218","author":"D. D. Haroske","year":"2013","unstructured":"Haroske, D. D., Skrzypczak, L.: Embeddings of Besov\u2013Morrey spaces on bounded domains. Studia Math., 218, 119\u2013144 (2013)","journal-title":"Studia Math."},{"key":"5104_CR12","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s13163-013-0143-1","volume":"27","author":"D. D. Haroske","year":"2014","unstructured":"Haroske, D. D., Skrzypczak, L.: On Sobolev and Franke\u2013Jawerth embeddings of smoothness Morrey spaces. Rev. Mat. Complut., 27, 541\u2013573 (2014)","journal-title":"Rev. Mat. Complut."},{"key":"5104_CR13","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1080\/03605309408821042","volume":"19","author":"H. Kozono","year":"1994","unstructured":"Kozono, H., Yamazaki, M.: Semilinear heat equations and the Navier\u2013Stokes equation with distributions in new function spaces as initial data. Comm. Partial Differential Equations, 19, 959\u20131014 (1994)","journal-title":"Comm. Partial Differential Equations"},{"issue":"185","key":"5104_CR14","first-page":"37","volume":"2014","author":"P. Li","year":"2014","unstructured":"Li, P., Xiao, J., Yang, Q.: Global mild solutions to modified Navier\u2013Stokes equations with small initial data in critical Besov-Q spaces. Electron. J. Differential Equations, 2014(185), 37 pp. (2014)","journal-title":"Electron. J. Differential Equations"},{"key":"5104_CR15","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1090\/S0002-9947-02-03214-2","volume":"355","author":"A. L. Mazzucato","year":"2003","unstructured":"Mazzucato, A. L.: Besov\u2013Morrey spaces: function space theory and applications to non-linear PDE. Trans. Amer. Math. Soc., 355, 1297\u20131364 (2003)","journal-title":"Trans. Amer. Math. Soc."},{"key":"5104_CR16","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1090\/S0002-9947-1938-1501936-8","volume":"43","author":"C. B. Morrey","year":"1938","unstructured":"Morrey, C. B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc., 43, 126\u2013166 (1938)","journal-title":"Trans. Amer. Math. Soc."},{"key":"5104_CR17","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0022-1236(69)90022-6","volume":"4","author":"J. Peetre","year":"1969","unstructured":"Peetre, J.: On the theory of L p,\u03bb spaces. J. Funct. Anal., 4, 71\u201387 (1969)","journal-title":"J. Funct. Anal."},{"key":"5104_CR18","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1002\/mana.201200020","volume":"286","author":"M. Rosenthal","year":"2013","unstructured":"Rosenthal, M.: Local means, wavelet bases, representations, and isomorphisms in Besov\u2013Morrey and Triebel\u2013Lizorkin\u2013Morrey spaces. Math. Nachr., 286, 59\u201387 (2013)","journal-title":"Math. Nachr."},{"issue":"1","key":"5104_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13163-013-0125-3","volume":"27","author":"M. Rosenthal","year":"2014","unstructured":"Rosenthal, M., Triebel, H.: Calder\u00f3n\u2013Zygmund operators in Morrey spaces. Rev. Mat. Complut., 27(1), 1\u201311 (2014)","journal-title":"Rev. Mat. Complut."},{"issue":"1","key":"5104_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13163-013-0145-z","volume":"28","author":"M. Rosenthal","year":"2015","unstructured":"Rosenthal, M., Triebel, H.: Morrey spaces, their duals and preduals. Rev. Mat. Complut., 28(1), 1\u201330 (2015)","journal-title":"Rev. Mat. Complut."},{"key":"5104_CR21","doi-asserted-by":"crossref","first-page":"93","DOI":"10.7169\/facm\/1229624654","volume":"38","author":"Y. Sawano","year":"2008","unstructured":"Sawano, Y.: Wavelet characterizations of Besov\u2013Morrey and Triebel\u2013Lizorkin\u2013Morrey spaces. Funct. Approx. Comment. Math., 38, 93\u2013107 (2008)","journal-title":"Funct. Approx. Comment. Math."},{"key":"5104_CR22","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1007\/s10114-009-8247-8","volume":"25","author":"Y. Sawano","year":"2009","unstructured":"Sawano, Y.: A note on Besov\u2013Morrey spaces and Triebel\u2013Lizorkin\u2013Morrey spaces. Acta Math. Sin., Engl. Ser., 25, 1223\u20131242 (2009)","journal-title":"Acta Math. Sin., Engl. Ser."},{"key":"5104_CR23","doi-asserted-by":"crossref","first-page":"91","DOI":"10.4064\/sm196-1-6","volume":"196","author":"Y. Sawano","year":"2010","unstructured":"Sawano, Y.: Brezis\u2013Gallou\u00ebt\u2013Wainger type inequality for Besov\u2013Morrey spaces. Studia Math., 196, 91\u2013101 (2010)","journal-title":"Studia Math."},{"key":"5104_CR24","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1007\/s00209-007-0150-3","volume":"257","author":"Y. Sawano","year":"2007","unstructured":"Sawano, Y., Tanaka, H., Decompositions of Besov\u2013Morrey spaces and Triebel\u2013Lizorkin\u2013Morrey spaces. Math. Z., 257, 871\u2013905 (2007)","journal-title":"Math. Z."},{"key":"5104_CR25","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1002\/mana.200610818","volume":"282","author":"Y. Sawano","year":"2009","unstructured":"Sawano, Y., Tanaka, H.: Besov\u2013Morrey spaces and Triebel\u2013Lizorkin\u2013Morrey spaces for non-doubling measures. Math. Nachr., 282, 1788\u20131810 (2009)","journal-title":"Math. Nachr."},{"key":"5104_CR26","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s00013-008-2802-x","volume":"92","author":"A. Seeger","year":"2009","unstructured":"Seeger, A., Trebels, W.: Low regularity classes and entropy numbers. Arch. Math., 92, 147\u2013157 (2009)","journal-title":"Arch. Math."},{"key":"5104_CR27","first-page":"110","volume":"3","author":"W. Sickel","year":"2012","unstructured":"Sickel, W.: Smoothness spaces related to Morrey spaces \u2014 a survey. I. Eurasian Math. J., 3, 110\u2013149 (2012)","journal-title":"I. Eurasian Math. J."},{"key":"5104_CR28","first-page":"82","volume":"4","author":"W. Sickel","year":"2013","unstructured":"Sickel, W.: Smoothness spaces related to Morrey spaces \u2014 a survey. II. Eurasian Math. J., 4, 82\u2013124 (2013)","journal-title":"II. Eurasian Math. J."},{"key":"5104_CR29","doi-asserted-by":"crossref","first-page":"105","DOI":"10.4171\/ZAA\/666","volume":"14","author":"W. Sickel","year":"1995","unstructured":"Sickel, W., Triebel, H.: H\u00f6lder inequalities and sharp embeddings in function spaces of Bs p,q and Fs p,q type. Z. Anal. Anwendungen, 14, 105\u2013140 (1995)","journal-title":"Z. Anal. Anwendungen"},{"key":"5104_CR30","first-page":"471","volume":"4","author":"S. L. Sobolev","year":"1938","unstructured":"Sobolev, S. L.: Sur un th\u00e9or\u00e8me d\u2019analyse fonctionnelle (in Russian). Mat. Sb., N. Ser. 4, 471\u2013497 (1938); English translation in: Amer. Math. Soc., Transl., II. Ser., 34, 39\u201368 (1963)","journal-title":"Mat. Sb., N. Ser."},{"key":"5104_CR31","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1002\/mana.200310281","volume":"278","author":"L. Tang","year":"2005","unstructured":"Tang, L., Xu, J.: Some properties of Morrey type Besov\u2013Triebel spaces. Math. Nachr., 278, 904\u2013917 (2005)","journal-title":"Math. Nachr."},{"key":"5104_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0346-0416-1","volume-title":"Theory of Function Spaces","author":"H. Triebel","year":"1983","unstructured":"Triebel, H.: Theory of Function Spaces, Birkh\u00e4user, Basel, 1983"},{"key":"5104_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0346-0419-2","volume-title":"Theory of Function Spaces. II","author":"H. Triebel","year":"1992","unstructured":"Triebel, H.: Theory of Function Spaces. II, Birkh\u00e4user, Basel, 1992"},{"key":"5104_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-0569-8","volume-title":"The Structure of Functions","author":"H. Triebel","year":"2001","unstructured":"Triebel, H.: The Structure of Functions, Birkh\u00e4user, Basel, 2001"},{"key":"5104_CR35","volume-title":"Theory of Function Spaces. III","author":"H. Triebel","year":"2006","unstructured":"Triebel, H.: Theory of Function Spaces. III, Birkh\u00e4user, Basel, 2006"},{"key":"5104_CR36","doi-asserted-by":"crossref","DOI":"10.4171\/123","volume-title":"Local Function Spaces, Heat and Navier\u2013Stokes Equations, EMS Tracts in Mathematics 20","author":"H. Triebel","year":"2013","unstructured":"Triebel, H.: Local Function Spaces, Heat and Navier\u2013Stokes Equations, EMS Tracts in Mathematics 20, European Mathematical Society (EMS), Z\u00fcrich, 2013"},{"key":"5104_CR37","doi-asserted-by":"crossref","DOI":"10.4171\/150","volume-title":"Hybrid Function Spaces, Heat and Navier\u2013Stokes Equations, EMS Tracts in Mathematics 24","author":"H. Triebel","year":"2015","unstructured":"Triebel, H.: Hybrid Function Spaces, Heat and Navier\u2013Stokes Equations, EMS Tracts in Mathematics 24, European Mathematical Society (EMS), Z\u00fcrich, 2015"},{"issue":"1","key":"5104_CR38","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1090\/S0002-9939-09-09832-3","volume":"138","author":"J. Vyb\u00edral","year":"2010","unstructured":"Vyb\u00edral, J.: On sharp embeddings of Besov and Triebel\u2013Lizorkin spaces in the subcritical case. Proc. Amer. Math. Soc., 138(1), 141\u2013146 (2010)","journal-title":"Proc. Amer. Math. Soc."},{"key":"5104_CR39","volume-title":"Holomorphic Q Classes, Lecture Notes in Math., 1767","author":"J. Xiao","year":"2001","unstructured":"Xiao, J.: Holomorphic Q Classes, Lecture Notes in Math., 1767, Springer, Berlin, 2001"},{"key":"5104_CR40","volume-title":"Geometric Qp Functions","author":"J. Xiao","year":"2006","unstructured":"Xiao, J.: Geometric Qp Functions, Birkh\u00e4user Verlag, Basel, 2006"},{"key":"5104_CR41","doi-asserted-by":"crossref","first-page":"2760","DOI":"10.1016\/j.jfa.2008.09.005","volume":"255","author":"D. Yang","year":"2008","unstructured":"Yang, D., Yuan, W.: A new class of function spaces connecting Triebel\u2013Lizorkin spaces and Q spaces. J. Funct. Anal., 255, 2760\u20132809 (2008)","journal-title":"J. Funct. Anal."},{"key":"5104_CR42","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s00209-009-0524-9","volume":"265","author":"D. Yang","year":"2010","unstructured":"Yang, D., Yuan, W.: New Besov-type spaces and Triebel\u2013Lizorkin-type spaces including Q spaces. Math. Z., 265, 451\u2013480 (2010)","journal-title":"Math. Z."},{"key":"5104_CR43","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1080\/00036811.2011.629610","volume":"92","author":"D. Yang","year":"2013","unstructured":"Yang, D., Yuan, W.: Relations among Besov-type spaces, Triebel\u2013Lizorkin-type spaces and generalized Carleson measure spaces. Appl. Anal., 92, 549\u2013561 (2013)","journal-title":"Appl. Anal."},{"key":"5104_CR44","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.jat.2014.12.006","volume":"192","author":"W. Yuan","year":"2015","unstructured":"Yuan, W., Haroske, D. D., Moura, S. D., et al.: Limiting embeddings in smoothness Morrey spaces, continuity envelopes and applications. J. Approx. Theory, 192, 306\u2013335 (2015)","journal-title":"J. Approx. Theory"},{"issue":"2","key":"5104_CR45","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1080\/00036811.2014.895331","volume":"94","author":"W. Yuan","year":"2015","unstructured":"Yuan, W., Haroske, D. D., Skrzypczak, L., et al.: Embedding properties of Besov-type spaces. Appl. Anal., 94(2), 318\u2013340 (2015)","journal-title":"Appl. Anal."},{"issue":"5","key":"5104_CR46","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1142\/S0219530514500493","volume":"13","author":"W. Yuan","year":"2015","unstructured":"Yuan, W., Haroske, D. D., Skrzypczak, L., et al.: Embedding properties of weighted Besov type spaces. Anal. Appl., 13(5), 507\u2013553 (2015)","journal-title":"Anal. Appl."},{"key":"5104_CR47","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/978-3-642-14606-0","volume-title":"Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics 2005","author":"W. Yuan","year":"2010","unstructured":"Yuan, W., Sickel, W., Yang, D.: Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics 2005, Springer-Verlag, Berlin, 2010, xi+281 pp"},{"key":"5104_CR48","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1002\/mana.201300020","volume":"286","author":"W. Yuan","year":"2013","unstructured":"Yuan, W., Sickel, W., Yang, D.: On the coincidence of certain approaches to smoothness spaces related to Morrey spaces. Math. Nachr., 286, 1571\u20131584 (2013)","journal-title":"Math. Nachr."}],"container-title":["Acta Mathematica Sinica, English Series"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10114-016-5104-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10114-016-5104-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10114-016-5104-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,13]],"date-time":"2020-09-13T18:34:44Z","timestamp":1600022084000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10114-016-5104-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,15]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["5104"],"URL":"https:\/\/doi.org\/10.1007\/s10114-016-5104-4","relation":{},"ISSN":["1439-8516","1439-7617"],"issn-type":[{"value":"1439-8516","type":"print"},{"value":"1439-7617","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,15]]}}}