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Two-weight norm inequalities for rough fractional integral operators on Morrey spaces

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Języki publikacji
EN
Abstrakty
EN
We establish the two-weight norm inequalities for the rough fractional integral operators on Morrey spaces.
Rocznik
Strony
67--77
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • The Education University of Hong Kong, Department of Mathematics and Information Technology, 10 Lo Ping Road, Tai Po, Hong Kong, China
Bibliografia
  • [1] D. Adams, A note on Riesz potentials, Duke Math. J. 42 (1975), 765–778.
  • [2] A. Almeida, J. Hasanov, S. Samko, Maximal and potential operators in variable exponent Morrey spaces, Georgian Math. J. 15 (2008), 195–208.
  • [3] Y. Ding, C.-C. Lin, Two-weight norm inequalities for the rough fractional integrals, Int. J. Math. Math. Sci. 25 (2001), 517–524.
  • [4] Y. Ding, S. Lu, Weighted norm inequalities for fractional integral operator with rough kernel, Canad. J. Math. 50 (1998), 29–39.
  • [5] V. Guliyev, J. Hasanov, S. Samko, Boundedness of maximal, potential type and singular integral operators in the generalized variable exponent Morrey type spaces, J. Math. Sci. (N.Y.) 170 (2010), 423–443.
  • [6] V. Guliyev, J. Hasanov, S. Samko, Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces, Math. Scand. 107 (2010), 285–304.
  • [7] K.-P. Ho, The fractional integral operators on Morrey spaces with variable exponent on unbounded domains, Math. Inequal. Appl. 16 (2013), 363–373.
  • [8] K.-P. Ho, Vector-valued operators with singular kernel and Treibel–Lizorkin block spaces with variable exponents, Kyoto J. Math. 56 (2016), 97–124.
  • [9] K.-P. Ho, Two-weight norm, Poincaré, Sobolev and Stein–Weiss inequalities on Morrey spaces, Publ. Res. Inst. Math. Sci. 53 (2017), 119–139.
  • [10] K.-P. Ho, Fractional integral operators with homogeneous kernels on Morrey spaces with variable exponents, J. Math. Soc. Japan 69 (2017), 1059–1077.
  • [11] K.-P. Ho, Singular integral operators with rough kernel on Morrey type spaces, Studia Math. 244 (2019), 217–243.
  • [12] K.-P. Ho, Weak type estimates of the fractional integral operators on Morrey spaces with variable exponents, Acta Appl. Math. 159 (2019), 1–10.
  • [13] K.-P. Ho, Potential type operators on weighted Morrey spaces, Arch. Math. 118 (2022), 159–168.
  • [14] Y. Komori, S. Shirai, Weighted Morrey spaces and a singular integral operator, Math. Nachr. 282 (2009), 219–231.
  • [15] B. Muckenhoupt, R. Wheeden, Weighted norm inequalities for singular and fractional integrals, Trans. Amer. Maths. Soc. 161 (1971), 249–258.
  • [16] E. Nakai, Generalized fractional integrals on Orlicz–Morrey spaces, [in:] Banach and Function Spaces, Yokohama Publishers, Yokohama, 2004, 323–333.
  • [17] E. Nakai, Orlicz–Morrey spaces and the Hardy-Littlewood maximal function, Studia Math. 188 (2008), 193–221.
  • [18] P. Olsen, Fractional integration, Morrey spaces and Schrödinger equation, Comm. Partial Differential Equations 20 (1995), 2005–2055.
  • [19] J. Peetre, On the theory of Lp,λ spaces, J. Funct. Anal. 4 (1969), 71–87.
  • [20] Y. Sawano, S. Sugano, H. Tanaka, Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces, Trans. Amer. Math. Soc. 363 (2011), 6481–6503.
  • [21] Y. Sawano, S. Sugano, H. Tanaka, Orlicz–Morrey spaces and fractional operators, Potent. Anal. 36 (2012), 517–556.
  • [22] H. Tanaka, Two-weight norm inequalities on Morrey spaces, Ann. Acad. Sci. Fenn. Math. 40 (2015), 773–791.
  • [23] H. Wang, Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces, J. Inequal. Appl. 2017 (2017), Article no. 6.
  • [24] X. Ye, T. Wang, Two-weighted norm inequalities of singular integral operators on weighted Morrey spaces, Georgian Math. J. 24 (2017), 629–638.
  • [25] T.-L. Yee, K.-P. Ho, Fractional integral operators with homogeneous kernels on generalized Lorentz-Morrey spaces, J. Math. Inequal. 15 (2021), 17–30.
  • [26] T.-L. Yee, K.-P. Ho, Two weighted norm inequalities of potential type operator on Herz spaces, Anal. Math. (to appear).
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7d6d3f1d-22d2-4732-ae6a-bffef0673c49
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