{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T04:12:41Z","timestamp":1758168761024,"version":"3.44.0"},"reference-count":31,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004239","name":"Poznan University of Technology","doi-asserted-by":"publisher","award":["0213\/SBAD\/0118"],"award-info":[{"award-number":["0213\/SBAD\/0118"]}],"id":[{"id":"10.13039\/501100004239","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Approximation Theory"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1016\/j.jat.2025.106214","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T23:35:34Z","timestamp":1753313734000},"page":"106214","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Embeddings of block-radial functions \u2014 approximation properties and nuclearity"],"prefix":"10.1016","volume":"312","author":[{"given":"Alicja","family":"Dota","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leszek","family":"Skrzypczak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jat.2025.106214_b1","first-page":"581","article-title":"Weighted Besov and Triebel space: Interpolation by the real method","volume":"12","author":"Bui","year":"1982","journal-title":"Hiroshima. Math. J."},{"key":"10.1016\/j.jat.2025.106214_b2","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1006\/jath.1998.3202","article-title":"About approximation numbers in function spaces","volume":"94","author":"Caetano","year":"1998","journal-title":"J. Approx. Theory"},{"key":"10.1016\/j.jat.2025.106214_b3","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1088\/1361-6544\/acb62d","article-title":"Radial and non-radial multiple solutions to a general mixed dispersion NLS equation","volume":"36","author":"d\u2019Avenia","year":"2023","journal-title":"Nonlinearity"},{"key":"10.1016\/j.jat.2025.106214_b4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jco.2018.10.005","article-title":"Some properties of block-radial functions and Schr\u00f6dinger type operators with block-radial potentials","volume":"53","author":"Dota","year":"2019","journal-title":"J. Complex."},{"year":"1996","author":"Edmunds","series-title":"Function Spaces, Entropy Numbers, Differential Operators","key":"10.1016\/j.jat.2025.106214_b5"},{"key":"10.1016\/j.jat.2025.106214_b6","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00041-001-4015-6","article-title":"An almost orthogonal radial wavelet expansion for radial distributions","volume":"1","author":"Epperson","year":"1995","journal-title":"J. Fourier Anal. Appl."},{"key":"10.1016\/j.jat.2025.106214_b7","doi-asserted-by":"crossref","first-page":"91","DOI":"10.4064\/bc92-0-7","article-title":"Gelfand and Kolmogorov numbers of embedding of radial Besov and Sobolev spaces","volume":"92","author":"Ga\u0327siorowska","year":"2011","journal-title":"Banach Center Publ."},{"key":"10.1016\/j.jat.2025.106214_b8","first-page":"196","article-title":"Produits tensoriels topologiques et espaces nucl\u00e9aires","volume":"16","author":"Grothendieck","year":"1955","journal-title":"Mem. Am. Math. Soc."},{"key":"10.1016\/j.jat.2025.106214_b9","doi-asserted-by":"crossref","first-page":"135","DOI":"10.5209\/rev_REMA.2008.v21.n1.16447","article-title":"Entropy and approximation number of embedding of function spaces with Muckenhoupt weights, I","volume":"21","author":"Haroske","year":"2008","journal-title":"Rev. Mat. Complut."},{"issue":"6","key":"10.1016\/j.jat.2025.106214_b10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s00020-020-02603-7","article-title":"Nuclear embeddings in weighted function spaces","volume":"92","author":"Haroske","year":"2020","journal-title":"Integral Equations Operator Theory"},{"key":"10.1016\/j.jat.2025.106214_b11","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1112\/S0024610702003848","article-title":"Compact embeddings of Besov spaces in exponential Orlicz spaces","volume":"67","author":"K\u00fchn","year":"2003","journal-title":"J. Lond. Math. Soc."},{"issue":"2","key":"10.1016\/j.jat.2025.106214_b12","doi-asserted-by":"crossref","first-page":"479","DOI":"10.5209\/rev_REMA.2005.v18.n2.16697","article-title":"Entropy numbers of general diagonal operators","volume":"18","author":"K\u00fchn","year":"2005","journal-title":"Rev. Mat. Complut."},{"key":"10.1016\/j.jat.2025.106214_b13","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/S0021-9045(02)00063-1","article-title":"Entropy numbers of Sobolev embeddings of radial Besov spaces","volume":"121","author":"K\u00fchn","year":"2003","journal-title":"J. Approx. Theory"},{"key":"10.1016\/j.jat.2025.106214_b14","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1017\/S0013091505000386","article-title":"Entropy numbers of embeddings of weighted Besov spaces II","volume":"49","author":"K\u00fchn","year":"2006","journal-title":"Proc. Edin. Math. Soc."},{"key":"10.1016\/j.jat.2025.106214_b15","first-page":"637","article-title":"Existence theorems for nonlinear elliptic problems in RN in the class of block-radial functions","volume":"30","author":"Kuzin","year":"1994","journal-title":"Differ. Equ."},{"year":"1997","author":"Kuzin","series-title":"Entire Solutions of Semilinear Elliptic Equations","key":"10.1016\/j.jat.2025.106214_b16"},{"key":"10.1016\/j.jat.2025.106214_b17","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0022-1236(82)90072-6","article-title":"Sym\u00e9trie et compacit\u00e9 dans les espaces de Sobolev","volume":"49","author":"Lions","year":"1982","journal-title":"J. Funct. Anal."},{"key":"10.1016\/j.jat.2025.106214_b18","series-title":"Operator Ideals","first-page":"20","author":"Pietsch","year":"1980"},{"issue":"2","key":"10.1016\/j.jat.2025.106214_b19","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1007\/BF01200378","article-title":"Grothendieck\u2019s concept of a p -nuclear operator","volume":"7","author":"Pietsch","year":"1984","journal-title":"Integr. Equ. Oper. Theory"},{"year":"1987","author":"Pietsch","series-title":"Eigenvalues and S-Numbers","key":"10.1016\/j.jat.2025.106214_b20"},{"year":"2007","author":"Pietsch","series-title":"History of Banach Spaces and Linear Operators","key":"10.1016\/j.jat.2025.106214_b21"},{"key":"10.1016\/j.jat.2025.106214_b22","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s00526-004-0302-9","article-title":"Non radial positive solutions for the H\u00e9non equation with critical growth","volume":"23","author":"Serra","year":"2005","journal-title":"Calc. Var."},{"key":"10.1016\/j.jat.2025.106214_b23","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/BF02510700","article-title":"Radial subspaces of Besov and Lizorkin-Triebel spaces: extended Strauss lemma and compactness of embeddings","volume":"6","author":"Sickel","year":"2000","journal-title":"J. Fourier Anal. A"},{"key":"10.1016\/j.jat.2025.106214_b24","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1142\/S0219199712500058","article-title":"On the interplay of regularity and decay in case of radial functions I. Inhomogeneous spaces","volume":"14","author":"Sickel","year":"2012","journal-title":"Comm. Contemp. Math."},{"issue":"1","key":"10.1016\/j.jat.2025.106214_b25","doi-asserted-by":"crossref","first-page":"417","DOI":"10.5186\/aasfm.2014.3918","article-title":"The radial Lemma of Strauss in the context of Morrey spaces","volume":"39","author":"Sickel","year":"2014","journal-title":"Ann. Acad. Sci. Fenn. Math."},{"key":"10.1016\/j.jat.2025.106214_b26","doi-asserted-by":"crossref","first-page":"267","DOI":"10.4171\/rmi\/319","article-title":"Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions","volume":"18","author":"Skrzypczak","year":"2002","journal-title":"Rev. Mat. Iberoamericana"},{"key":"10.1016\/j.jat.2025.106214_b27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s00041-018-9593-7","article-title":"Pointwise estimates of Block-Radial functions of Sobolev Classes","volume":"25","author":"Skrzypczak","year":"2019","journal-title":"J. Fourier Anal. Appl."},{"key":"10.1016\/j.jat.2025.106214_b28","first-page":"237","article-title":"Approximation numbers of Sobolev embeddings between radial Besov and Sobolev spaces","author":"Skrzypczak","year":"2004","journal-title":"Comment. Mat. Pr. Mat. Tomus Spec. Honor. Juliani Musielak"},{"key":"10.1016\/j.jat.2025.106214_b29","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BF01626517","article-title":"Existence of solitary waves in higher dimensions","volume":"55","author":"Strauss","year":"1977","journal-title":"Comm. Math. Phys."},{"key":"10.1016\/j.jat.2025.106214_b30","first-page":"235","article-title":"Diagonal nuclear operators on lp spaces","volume":"143","author":"Tong","year":"1969","journal-title":"Trans. Amer. Math. Soc."},{"year":"1983","author":"Triebel","series-title":"Theory of Function Spaces","key":"10.1016\/j.jat.2025.106214_b31"}],"container-title":["Journal of Approximation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021904525000723?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021904525000723?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T21:10:58Z","timestamp":1758143458000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021904525000723"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12]]},"references-count":31,"alternative-id":["S0021904525000723"],"URL":"https:\/\/doi.org\/10.1016\/j.jat.2025.106214","relation":{},"ISSN":["0021-9045"],"issn-type":[{"type":"print","value":"0021-9045"}],"subject":[],"published":{"date-parts":[[2025,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Embeddings of block-radial functions \u2014 approximation properties and nuclearity","name":"articletitle","label":"Article Title"},{"value":"Journal of Approximation Theory","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jat.2025.106214","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"106214"}}