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Spherical Maximal Function on Local Morrey Spaces with Variable Exponents

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Abstract

We establish the boundedness of the spherical maximal function on local Morrey spaces with variable exponents.

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References

  1. Almeida, A., Hasanov, J., Samko, S.: Maximal and potential operators in variable exponent Morrey spaces. Georgian Math. J. 15, 195–208 (2008)

    Article  MathSciNet  Google Scholar 

  2. Burenkov, V.I., Guliyev, H.V.: Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. Stud. Math. 163, 157–176 (2004)

    Article  MathSciNet  Google Scholar 

  3. Burenkov, V.I., Guliyev, H.V., Guliyev, V.S.: Necessary and sufficient conditions for boundedness of fractional maximal operators in local Morrey-type spaces. J. Comput. Appl. Math. 208, 280–301 (2007)

    Article  MathSciNet  Google Scholar 

  4. Burenkov, V.I., Guliyev, V.S., Tararykova, T.V., Serbetci, A.: Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces. Dokl. Akad. Nauk 422, 11–14 (2008)

    Google Scholar 

  5. Burenkov, V., Gogatishvili, A., Guliyev, V.S., Mustafayev, R.: Boundedness of the fractional maximal operator in local Morrey-type spaces. Complex Var. Elliptic Equ. 55, 739–758 (2010)

    Article  MathSciNet  Google Scholar 

  6. Burenkov, V., Nursultanov, E.: Description of interpolation spaces for local Morrey-type spaces. Proc. Steklov Inst. Math. 269, 46–56 (2010)

    Article  MathSciNet  Google Scholar 

  7. Cowling, M., García-Cuerva, J., Gunawan, H.: Weighted estimates for fractional maximal functions related to spherical means. Bull. Aust. Math. Soc. 66, 75–90 (2002)

    Article  MathSciNet  Google Scholar 

  8. Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue Spaces. Birkhäuser, Basel (2013)

    Book  Google Scholar 

  9. Diening, L.: Maximal functions on generalized Lebesgue spaces Lp(⋅). Math. Inequal. Appl. 7, 245–253 (2004)

    MathSciNet  Google Scholar 

  10. Diening, L., Harjulehto, P., Hästö, P., Ružička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Springer, Berlin (2011)

    Book  Google Scholar 

  11. Duoandikoetxea, J., Vega, L.: Spherical means and weighted inequalities. J. Lond. Math. Soc. 53, 343–353 (1996)

    Article  MathSciNet  Google Scholar 

  12. Duoandikoetxea, J., Moyua, A., Oruetxebarria, O.: The spherical maximal operator on radial functions. J. Math. Anal. Appl. 387, 655–666 (2012)

    Article  MathSciNet  Google Scholar 

  13. Fiorenza, A., Gogatishvili, A., Kopaliani, T.: Boundedness of Stein’s spherical maximal function in variable Lebesgue spaces and application to the wave equation. Arch. Math. 100, 465–472 (2013)

    Article  MathSciNet  Google Scholar 

  14. Gogatishvili, A., Mustafayev, R.: Dual spaces of local Morrey-type spaces. Czech. Math. J. 61, 609 (2011)

    Article  MathSciNet  Google Scholar 

  15. Guliyev, V.S., Hasanov, J.J., Samko, S.G.: Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces. Math. Scand. 107, 285–304 (2010)

    Article  MathSciNet  Google Scholar 

  16. Guliyev, V.S.: Generalized local Morrey spaces and fractional integral operators with rough kernel. J. Math. Sci. 193, 211–227 (2013)

    Article  MathSciNet  Google Scholar 

  17. Gunawan, H.: On weighted estimates for Stein’s maximal function. Bull. Aust. Math. Soc. 54, 35–39 (1996)

    Article  MathSciNet  Google Scholar 

  18. Gunawan, H.: Some weighted estimates for Stein’s maximal function. Bull. Malays. Math. Soc. 21, 101–105 (1998)

    MathSciNet  Google Scholar 

  19. Ho, K.-P.: Extrapolation, John-Nirenberg inequalities and characterizations of BMO in terms of Morrey type spaces. Rev. Mat. Complut. 30, 487–505 (2017)

    Article  MathSciNet  Google Scholar 

  20. Ho, K.-P.: Stein–weiss inequalities for radial local Morrey spaces. Port. Math. 76, 301–310 (2019)

    Article  MathSciNet  Google Scholar 

  21. Ho, K.-P.: Spherical maximal functions, variation and oscillation inequalities on Herz spaces. Arab J. Basic Appl. Sci. 26, 72–77 (2019)

    Article  Google Scholar 

  22. Ho, K.-P.: Extrapolation to Herz spaces with variable exponents and applications. Rev. Mat. Complut. 33, 437–463 (2020)

    Article  MathSciNet  Google Scholar 

  23. Ho, K.-P.: Spherical maximal function, maximal Bochner–Riesz mean and geometrical maximal function on Herz spaces with variable exponents. Rend. Circ. Mat. Palermo, II Ser. 70, 559–574 (2021)

    Article  MathSciNet  Google Scholar 

  24. Ho, K.-P.: Singular integral operators and sublinear operators on Hardy local Morrey spaces with variable exponents. Bull. Sci. Math. 171, 103033 (2021)

    Article  MathSciNet  Google Scholar 

  25. Ho, K.-P.: Extrapolation to weighted Morrey spaces with variable exponents and applications. Proc. Edinb. Math. Soc. 64, 1002–1027 (2021)

    Article  MathSciNet  Google Scholar 

  26. Ho, K.-P.: Calderón operator on local Morrey spaces with variable exponents. Mathematics 9, 2977 (2021)

    Article  Google Scholar 

  27. Ho, K.-P.: Boundedness of operators and inequalities on Morrey-Banach spaces. Publ. Res. Inst. Math. Sci. (2021)

  28. John, F.: Plane Waves and Spherical Means: Applied to Partial Differential Equations. Interscience Publishers, New York (1955)

    Google Scholar 

  29. Kokilashvili, V., Meskhi, A.: Boundedness of maximal and singular operators in Morrey spaces with variable exponent. Armen. J. Math. 1, 18–28 (2008)

    MathSciNet  Google Scholar 

  30. Kokilashvili, V., Meskhi, A.: Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. Complex Var. Elliptic Equ. 55, 923–936 (2010)

    Article  MathSciNet  Google Scholar 

  31. Manna, R.: Weighted inequalities for spherical maximal operator. Proc. Jpn. Acad. Ser. A Math. Sci. 91, 135–140 (2015)

    Article  MathSciNet  Google Scholar 

  32. Morrey, C.B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43, 126–166 (1938)

    Article  MathSciNet  Google Scholar 

  33. Nakai, E.: Hardy–littlewood maximal operator, singular integral operators and Riesz potentials on generalized Morrey spaces. Math. Nachr. 166, 95–103 (1994)

    Article  MathSciNet  Google Scholar 

  34. Rubio de Francia, J.L.: Factorization and extrapolation of weights. Bull. Amer. Math. Soc. (N.S.) 7, 393–395 (1982)

    Article  MathSciNet  Google Scholar 

  35. Rubio de Francia, J.L.: A new technique in the theory of Ap weights. In: Topics in Modern Harmonic Analysis, Vol. I, II (Turin/Milan, (1982), pp. 571–579. Ist. Naz. Alta Mat. Francesco Severi, Rome (1983)

  36. Rubio de Francia, J.L.: Factorization theory and ap weights. Amer. J. Math. 106, 533–547 (1984)

    Article  MathSciNet  Google Scholar 

  37. Stein, E.M.: Maximal functions: spherical means. Proc. Nat. Acad. Sci. USA 73, 2174–2175 (1976)

    Article  MathSciNet  Google Scholar 

  38. Yee, T.-L., Cheung, K.L., Ho, K.-P., Suen, C.K.: Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents. Math. Inequal. Appl. 23, 1509–1528 (2020)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China

    Tat-Leung Yee, Ka Luen Cheung, Kwok-Pun Ho & Chun Kit Suen

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  1. Tat-Leung Yee
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  2. Ka Luen Cheung
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  3. Kwok-Pun Ho
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  4. Chun Kit Suen
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Correspondence to Kwok-Pun Ho.

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Yee, TL., Cheung, K.L., Ho, KP. et al. Spherical Maximal Function on Local Morrey Spaces with Variable Exponents. Vietnam J. Math. 52, 107–115 (2024). https://doi.org/10.1007/s10013-022-00563-6

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  • DOI: https://doi.org/10.1007/s10013-022-00563-6

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