Tohoku Mathematical Journal

Boundedness of the maximal operator on Musielak-Orlicz-Morrey spaces

Fumi-Yuki Maeda, Takao Ohno, and Tetsu Shimomura

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Abstract

We give the boundedness of the maximal operator on Musielak-Orlicz-Morrey spaces, which is an improvement of [7, Theorem 4.1]. We also discuss the sharpness of our conditions.

Article information

Source
Tohoku Math. J. (2), Volume 69, Number 4 (2017), 483-495.

Dates
First available in Project Euclid: 2 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1512183626

Digital Object Identifier
doi:10.2748/tmj/1512183626

Mathematical Reviews number (MathSciNet)
MR3732884

Zentralblatt MATH identifier
06850810

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

Keywords
maximal operator Musielak-Orlicz-Morrey space variable exponent

Citation

Maeda, Fumi-Yuki; Ohno, Takao; Shimomura, Tetsu. Boundedness of the maximal operator on Musielak-Orlicz-Morrey spaces. Tohoku Math. J. (2) 69 (2017), no. 4, 483--495. doi:10.2748/tmj/1512183626. https://projecteuclid.org/euclid.tmj/1512183626


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References

  • A. Almeida, J. Hasanov and S. Samko, Maximal and potential operators in variable exponent Morrey spaces, Georgian Math. J. 15 (2008), no. 2, 195–208.
  • D. Cruz-Uribe and A. Fiorenza, Variable Lebesgue spaces, Foundations and harmonic analysis, Applied and Numerical Harmonic Analysis, Birkhauser/Springer, Heidelberg, 2013.
  • D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, The maximal function on variable $L^p$ spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), 223–238; Ann. Acad. Sci. Fenn. Math. 29 (2004), 247–249.
  • L. Diening, Maximal functions in generalized $L^{p(\cdot)}$ spaces, Math. Inequal. Appl. 7(2) (2004), 245–254.
  • L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Math. 2017, Springer, 2011.
  • P. Hästö, The maximal operator on generalized Orlicz spaces, J. Funct. Anal. 269 (2015), no. 12, 4038–4048; Corrigendum to “The maximal operator on generalized Orlicz spaces”, J. Funct. Anal. 271 (2016), no. 1, 240–243.
  • F.-Y. Maeda, Y. Mizuta, T. Ohno and T. Shimomura, Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces, Bull. Sci. Math. 137 (2013), 76–96.
  • Y. Mizuta and T. Shimomura, Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent, J. Math. Soc. Japan 60 (2008), 583–602.
  • J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, 1983.
  • E. Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr. 166 (1994), 95–103.
  • E. Nakai, Generalized fractional integrals on Orlicz-Morrey spaces, Banach and function spaces, 323–333, Yokohama Publ., Yokohama, 2004.
  • H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen Co., Ltd., Tokyo, 1950.