{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T04:19:41Z","timestamp":1775362781687,"version":"3.50.1"},"reference-count":24,"publisher":"Allerton Press","issue":"6","license":[{"start":{"date-parts":[[2011,5,25]],"date-time":"2011-05-25T00:00:00Z","timestamp":1306281600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2011,5,25]],"date-time":"2011-05-25T00:00:00Z","timestamp":1306281600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Russ Math."],"published-print":{"date-parts":[[2011,6]]},"DOI":"10.3103\/s1066369x11060041","type":"journal-article","created":{"date-parts":[[2011,5,24]],"date-time":"2011-05-24T00:44:30Z","timestamp":1306197870000},"page":"20-28","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Zygmund-type estimates for fractional integration and differentiation operators of variable order"],"prefix":"10.3103","volume":"55","author":[{"given":"B. G.","family":"Vakulov","sequence":"first","affiliation":[]},{"given":"E. S.","family":"Kochurov","sequence":"additional","affiliation":[]},{"given":"N. G.","family":"Samko","sequence":"additional","affiliation":[]}],"member":"1627","published-online":{"date-parts":[[2011,5,25]]},"reference":[{"key":"9263_CR1","volume-title":"Introduction to Theory of Nonlinear Singular Equations","author":"A. I. Guseinov","year":"1980","unstructured":"A. I. Guseinov and H. Sh. Mukhtarov, Introduction to Theory of Nonlinear Singular Equations (Nauka, Moscow, 1980)."},{"issue":"4","key":"9263_CR2","first-page":"439","volume":"339","author":"N. K. Karapetyants","year":"1994","unstructured":"N. K. Karapetyants and A. I. Ginzburg, \u201cFractional Integrodifferentiation in H\u00f6lder Classes of Variable Order,\u201d Phys. Dokl. 339(4), 439\u2013441 (1994).","journal-title":"Phys. Dokl."},{"issue":"2","key":"9263_CR3","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/BF02257475","volume":"2","author":"N. K. Karapetyants","year":"1995","unstructured":"N. K. Karapetyants and A. I. Ginzburg, \u201cFractional Integrodifferentiation in H\u00f6lder Classes of Arbitrary Order,\u201d Georg. Math. J. 2(2), 141\u2013150 (1995).","journal-title":"Georg. Math. J."},{"issue":"4","key":"9263_CR4","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1155\/S0161171295001001","volume":"18","author":"B. Ross","year":"1995","unstructured":"B. Ross and S. G. Samko, \u201cFractional Integration Operator of Variable Order in the H\u00f6lder Spaces H\n                           \u03bb(x),\u201d Intern. J.Math. and Math. Sci. 18(4), 777\u2013788 (1995).","journal-title":"Intern. J.Math. and Math. Sci."},{"key":"9263_CR5","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1090\/conm\/212\/02884","volume":"212","author":"S. G. Samko","year":"1998","unstructured":"S. G. Samko, \u201cDifferentiation and Integration of Variable Order and the Spaces L\n                           p(x),\u201d Contemporary Math. 212, 203\u2013219 (1998).","journal-title":"Contemporary Math."},{"issue":"1","key":"9263_CR6","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/s10634-005-0016-5","volume":"400","author":"B. G. Vakulov","year":"2005","unstructured":"B. G. Vakulov, \u201cSpherical Potentials in Weighted H\u00f6lder Spaces of Variable Order,\u201d Dokl. Phys. 400(1), 7\u201310 (2005).","journal-title":"Dokl. Phys."},{"issue":"2","key":"9263_CR7","first-page":"26","volume":"7","author":"B. G. Vakulov","year":"2005","unstructured":"B. G. Vakulov, \u201cSpherical Operators of Potential Type in Weighted H\u00f6lder Spaces of Variable Order,\u201d Vladikavkazsk. Matem. Zhurn. 7(2), 26\u201340 (2005).","journal-title":"Vladikavkazsk. Matem. Zhurn."},{"key":"9263_CR8","unstructured":"B. G. Vakulov, \u201cSpherical Convolution Operators with a Power-Logarithmic Kernel in of Generalized H\u00f6lder Spaces with Variable Characteristic,\u201d Izv. Vyssh. Uchebn. Zaved. Severo-Kavkazsk. Region. Estestv. Nauki, No. 1, 7\u201310 (2006)."},{"issue":"5","key":"9263_CR9","doi-asserted-by":"crossref","first-page":"683","DOI":"10.4213\/mzm3077","volume":"80","author":"B. G. Vakulov","year":"2006","unstructured":"B. G. Vakulov, \u201cSpherical Convolution Operators in Spaces of Variable H\u00f6lder Order,\u201d Matem. Zametki 80(5), 683\u2013695 (2006).","journal-title":"Matem. Zametki"},{"issue":"5\u20136","key":"9263_CR10","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1080\/10652460412331310304","volume":"16","author":"B. G. Vakulov","year":"2005","unstructured":"B. G. Vakulov, \u201cSpherical Potentials of Complex Order in the Variable Order H\u00f6lder Spaces,\u201d Integral Transforms and Special Functions 16(5\u20136), 489\u2013497 (2005).","journal-title":"Integral Transforms and Special Functions"},{"key":"9263_CR11","unstructured":"B. G. Vakulov, N. G. Samko, and S. G. Samko, \u201cPotential Type Operators and Hypersingular Integrals in Variable Order H\u00f6lder Spaces on Homogeneous Spaces,\u201d Izv. Vyssh. Uchebn. Zaved. Severo-Kavkazsk. Region. Estestv. Nauki. Sovremen. Problemy Matem. Gidrodinamiki, Special Issue, 40\u201345 (2009)."},{"issue":"4","key":"9263_CR12","first-page":"437","volume":"7","author":"N. K. Karapetyants","year":"2004","unstructured":"N. K. Karapetyants and N.G. Samko, \u201cWeighted Theorems on Fractional Integrals in the Generalized H\u00f6lder Spaces H\n                           \u03c90(\u03f1) via the Indices m\n                           \u03c9 and M\n                           \u03c9,\u201d Fract. Calc. Appl. Anal. 7(4), 437\u2013458 (2004).","journal-title":"Fract. Calc. Appl. Anal."},{"key":"9263_CR13","first-page":"483","volume":"5","author":"N.K. Bari","year":"1956","unstructured":"N.K. Bari and S. B. Stechkin, \u201cBest Approximation and Differential Properties of Two Conjugate Functions,\u201d Trudy Mosk. Matem. Ob-va, 5, 483\u2013522 (1956).","journal-title":"Trudy Mosk. Matem. Ob-va"},{"key":"9263_CR14","unstructured":"S. G. Samko and Kh. M. Murdaev, \u201cWeighted Zygmund Estimates for Fractional Differentiation and Integration, and Their Applications,\u201d Trudy Steklov Math. Inst, No. 3, 233\u2013235 (1989)."},{"key":"9263_CR15","volume-title":"Orlicz Spaces and Interpolation","author":"L. Maligranda","year":"1989","unstructured":"L. Maligranda, Orlicz Spaces and Interpolation (Departamento de Matem \u00e1 tica, Universidade Estadual de Campinas, Campinas SP Brazil, 1989)."},{"key":"9263_CR16","doi-asserted-by":"crossref","unstructured":"W. Matuszewska and W. Orlicz, \u201cOn Some Classes of Functions with Regard to Their Orders of Growth,\u201d Studia Math., No. 26, 11\u201324 (1965).","DOI":"10.4064\/sm-26-1-11-24"},{"key":"9263_CR17","first-page":"107","volume":"120","author":"N. G. Samko","year":"1999","unstructured":"N. G. Samko, \u201cSingular Integral Operators in Weighted Spaces with Generalized H\u00f6lder Condition,\u201d Proc. A. Razmadze Math. Inst., Tbilisi 120, 107\u2013134 (1999).","journal-title":"Proc. A. Razmadze Math. Inst., Tbilisi"},{"key":"9263_CR18","first-page":"363","volume-title":"Proceedings of IWOTA 2000, Setembro 12\u201315, Faro, Portugal","author":"N. G. Samko","year":"2002","unstructured":"N. G. Samko, \u201cCriterion of Fredholmness of Singular Operators with Piece-Wise Continuous Coefficients in the Generalized H\u00f6lder Spaces with Weight,\u201d in Proceedings of IWOTA 2000, Setembro 12\u201315, Faro, Portugal, (Operator Theory: Advances and Applications, Birkhauser, 2002), Vol. 142, pp. 363\u2013376."},{"key":"9263_CR19","first-page":"91","volume":"136","author":"N. G. Samko","year":"2004","unstructured":"N. G. Samko, \u201cOn Compactness of Integral Operators with a Generalized Weak Singularity in Weighted Spaces of Continuous Functions with a Given Continuity Modulus,\u201d Proc. A. Razmadze Math. Inst., Tbilisi 136, 91\u2013113 (2004).","journal-title":"Proc. A. Razmadze Math. Inst., Tbilisi"},{"issue":"2","key":"9263_CR20","doi-asserted-by":"crossref","first-page":"727","DOI":"10.14321\/realanalexch.30.2.0727","volume":"30","author":"N.G. Samko","year":"2005","unstructured":"N.G. Samko, \u201cOn Non-Equilibrated Almost Monotonic Functions of the Zygmund-Bari-Stechkin Class,\u201d Real Anal. Exch. 30(2), 727 (2005).","journal-title":"Real Anal. Exch."},{"key":"9263_CR21","first-page":"323","volume-title":"Proc. of IWOTA, Newcastle, July 2004","author":"N.G. Samko","year":"2006","unstructured":"N.G. Samko, \u201cSingular Integral Operators in Weighted Spaces of Continuous Functions with an Oscillating Continuity Modulus and Oscillating Weights,\u201d in Proc. of IWOTA, Newcastle, July 2004 (Operator Theory: Advances and Applications, Birkhauser, 2006), Vol. 171, pp. 323\u2013347."},{"issue":"12","key":"9263_CR22","doi-asserted-by":"publisher","first-page":"1359","DOI":"10.1002\/mana.200410425","volume":"279","author":"N. G. Samko","year":"2006","unstructured":"N. G. Samko, \u201cSingular Integral Operators in Weighted Spaces of Continuous Functions with Non-Equilibrated Continuity Modulus,\u201d Math. Nachrichten, Weinheim 279(12), 1359\u20131375 (2006).","journal-title":"Math. Nachrichten, Weinheim"},{"key":"9263_CR23","first-page":"122","volume":"145","author":"N. G. Samko","year":"2007","unstructured":"N. G. Samko, \u201cParameter Depending Bari-Stechkin Classes and Local Dimensions of Measure Metric Spaces,\u201d Proc. A. Razmadze Math. Inst., Tbilisi 145, 122\u2013129 (2007).","journal-title":"Proc. A. Razmadze Math. Inst., Tbilisi"},{"issue":"1","key":"9263_CR24","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1155\/2009\/929041","volume":"7","author":"N. G. Samko","year":"2009","unstructured":"N. G. Samko, \u201cParameter Depending Almost Monotonic Functions and Their Applications to Dimensions in Metric Measure Spaces,\u201d J. Function Spaces Appl. 7(1), 61\u201389 (2009).","journal-title":"J. Function Spaces Appl."}],"container-title":["Russian Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S1066369X11060041.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.3103\/S1066369X11060041","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.3103\/S1066369X11060041","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.3103\/S1066369X11060041.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T03:28:44Z","timestamp":1775359724000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.3103\/S1066369X11060041"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,25]]},"references-count":24,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2011,6]]}},"alternative-id":["9263"],"URL":"https:\/\/doi.org\/10.3103\/s1066369x11060041","relation":{},"ISSN":["1066-369X","1934-810X"],"issn-type":[{"value":"1066-369X","type":"print"},{"value":"1934-810X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5,25]]},"assertion":[{"value":"30 December 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2011","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}