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Tytuł artykułu

Zygmund inequality of the conjugate function on Morrey-Zygmund spaces

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Języki publikacji
EN
Abstrakty
EN
We generalize the Zygmund inequality for the conjugate function to the Morrey type spaces defined on the unit circle T. We obtain this extended Zygmund inequality by introducing the Morrey-Zygmund space on T.
Wydawca
Rocznik
Strony
97--104
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
  • Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China
autor
  • Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China
Bibliografia
  • [1] Zygmund A., Sur les fonctions conjugées, C. R. Acad. Sci. Paris, 1928, 187, 1025–1026
  • [2] Bennett C., Sharpley R., Interpolation of Operators, Academic Press, 1988
  • [3] Morrey C., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., 1938, 43, 126–166
  • [4] Adams D., A note on Riesz potentials, Duke Math. J., 1975, 42, 765–778
  • [5] Chiarenza F., Frasca M., Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. Appl., 1987, 7, 273–279
  • [6] Gogatishvili A., Mustafayev R. Ch., A note on boundedness of the Hardy-Littlewood maximal operator on Morrey spaces, Mediterr. J. Math., 2016, 13(4), 1885–1891
  • [7] Nakai E., Hardy-Littlewood maximal operator, singular integral operators and the Reisz potentials on generalized Morrey spaces, Math. Nachr., 1994, 166, 95–104
  • [8] Sawano Y., Sugano S., Tanaka H., Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces, Trans. Amer. Math. Soc., 2011, 363(12), 6481–6503
  • [9] Ho K.-P., Two-weight norm, Poincaré, Sobolev and Stein-Weiss inequalities on Morrey spaces, Publ. RIMS Kyoto Univ., 2017, 53(1), 119–139
  • [10] Tanaka H., Two-weight norm inequalities on Morrey spaces, Ann. Acad. Sci. Fenn. Math., 2015, 40, 773–791
  • [11] Izumi T., Sato E., Yabuta K., Remarks on a subspace of Morrey spaces, Tokyo J. Math., 2014, 37(1), 185–197
  • [12] Sawano Y., Sugano S., Tanaka H., A note on generalized fractional integral operators on Orlicz-Morrey spaces, Potential Anal., 2012, 36, 517–556
  • [13] Torchinsky A., Real-variable Methods in Harmonic Analysis, Dover Publications, Inc., 2004
  • [14] Deringoz F., Guliyev V. S., Samko S., Boundedness of maximal and singular operators on generalized Orlicz-Morrey spaces, In: Operator Theory, Operator Algebras and Applications, Series: Operator Theory: Advances and Applications, 2014, 242, 139–158
  • [15] Ho K.-P., Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces, Ann. Acad. Sci. Fenn. Math., 2012, 37, 375–406
  • [16] Ho K.-P., Extrapolation, John-Nirenberg inequalities and characterizations of BMO in terms of Morrey type spaces, Rev. Mat. Complut., 2017, 30(3), 487–505
  • [17] Ho K.-P., The Ahlfors-Beurling transform on Morrey spaces with variable exponents, Integral Trans. Spec. Funct., 2018, 29(3), 207–220
  • [18] Ho K.-P., Singular integral operators with rough kernel on Morrey type spaces, Studia Math., 2019, 244, 217–243
  • [19] Ho K.-P., Definability of singular integral operators on Morrey-Banach spaces, J. Math Soc. Japan, 2018, (published online)
  • [20] Ho K.-P., Weak type estimates of singular integral operators on Morrey type spaces, (preprint)
  • [21] Rosenthal M., Schmeisser H.-J., The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality, Rev. Mat. Complut., 2016, 29(3), 623–657
  • [22] Sawano Y., El-Shabrawy S., Weak Morrey spaces with applications, Math. Nachr., 2018, 291(1), 178–186, https://doi.org/10.1002/mana.201700001
  • [23] Gogatishvili A., Mustafayev R. Ch., Agcayazi M., Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function, Tokyo J. Math., 2018, 41(1), 193–218
  • [24] Nakamura S., Generalized weighted Morrey spaces and classical operators, Math. Nachr., 2016, 289(17-18), 2235–2262
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a9737122-f2f4-4757-84f3-27946c6f696e
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