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Year 2019, Volume: 2 Issue: 1, 37 - 40, 30.10.2019

Lütfi Akın

Abstract

References

  • [1] C. Capone, D. Cruz-Uribe, A. Fiorenza, The fractional maximal operator and fractional integrals on variable Lp spaces. Rev. Mat. Iberoam. 23 (2007), 743-770.
  • [2] D. Cruz-Uribe, A. Fiorenza,Variable Lebesgue Spaces. Birkhuser, Basel, 2013.
  • [3] E. Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math. Nachr. 166 (1994), 95-104.
  • [4] K.P. Ho, Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces,Sci. China Math.60 (2017), 449-468.
  • [5] K.P. Ho, Weak Type Estimates of the Fractional Integral Operators on Morrey Spaces with Variable Exponents, Acta Appl Math. 159 (2019), 1-10
  • [6] K.P. Ho, The fractional integral operators on Morrey spaces with variable exponent on unbounded domains, Math. Inequal. Appl. 16(2013), 363-373.
  • [7] L. Ferreira, On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations, J. Math. Pures Appl. 9(105) (2016), 228-247.
  • [8] L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponent, Lecture Notes in Mathematics, 2017 (2011), Springer.
  • [9] 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.
  • [10] Y. Mizuta, T. Shimomura, Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent, J. Math. Soc. Jpn. 60(2008), 583-602.
  • [11] Y. Sawano, S. Sugano, H. Tanaka, Orlicz-Morrey spaces and fractional operators, Potential Anal. 36 (2012), 517-556.

Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces

Year 2019, Volume: 2 Issue: 1, 37 - 40, 30.10.2019

Lütfi Akın

Abstract

We show that when the infimum of the exponent function, Hardy integral operator is a bounded operator from the Morrey space with variable exponent to the weak Morrey space with variable exponent.

Keywords

Hardy integral operator Morrey spaces Weak Morrey spaces Variable exponent

References

  • [1] C. Capone, D. Cruz-Uribe, A. Fiorenza, The fractional maximal operator and fractional integrals on variable Lp spaces. Rev. Mat. Iberoam. 23 (2007), 743-770.
  • [2] D. Cruz-Uribe, A. Fiorenza,Variable Lebesgue Spaces. Birkhuser, Basel, 2013.
  • [3] E. Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math. Nachr. 166 (1994), 95-104.
  • [4] K.P. Ho, Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces,Sci. China Math.60 (2017), 449-468.
  • [5] K.P. Ho, Weak Type Estimates of the Fractional Integral Operators on Morrey Spaces with Variable Exponents, Acta Appl Math. 159 (2019), 1-10
  • [6] K.P. Ho, The fractional integral operators on Morrey spaces with variable exponent on unbounded domains, Math. Inequal. Appl. 16(2013), 363-373.
  • [7] L. Ferreira, On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations, J. Math. Pures Appl. 9(105) (2016), 228-247.
  • [8] L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponent, Lecture Notes in Mathematics, 2017 (2011), Springer.
  • [9] 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.
  • [10] Y. Mizuta, T. Shimomura, Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent, J. Math. Soc. Jpn. 60(2008), 583-602.
  • [11] Y. Sawano, S. Sugano, H. Tanaka, Orlicz-Morrey spaces and fractional operators, Potential Anal. 36 (2012), 517-556.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Lütfi Akın 0000-0002-5653-9393

Publication Date October 30, 2019
Acceptance Date October 1, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Akın, L. (2019). Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces. Conference Proceedings of Science and Technology, 2(1), 37-40.
AMA Akın L. Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces. Conference Proceedings of Science and Technology. October 2019;2(1):37-40.
Chicago Akın, Lütfi. “Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue Spaces”. Conference Proceedings of Science and Technology 2, no. 1 (October 2019): 37-40.
EndNote Akın L (October 1, 2019) Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces. Conference Proceedings of Science and Technology 2 1 37–40.
IEEE L. Akın, “Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces”, Conference Proceedings of Science and Technology, vol. 2, no. 1, pp. 37–40, 2019.
ISNAD Akın, Lütfi. “Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue Spaces”. Conference Proceedings of Science and Technology 2/1 (October 2019), 37-40.
JAMA Akın L. Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces. Conference Proceedings of Science and Technology. 2019;2:37–40.
MLA Akın, Lütfi. “Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue Spaces”. Conference Proceedings of Science and Technology, vol. 2, no. 1, 2019, pp. 37-40.
Vancouver Akın L. Weak Type Estimates Of Hardy Integral Operators On Morrey Spaces With Variable Exponent Lebesgue spaces. Conference Proceedings of Science and Technology. 2019;2(1):37-40.
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