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

Öz

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.

Anahtar Kelimeler

• Hardy integral operator,Morrey spaces,Weak Morrey spaces,Variable exponent

Kaynakça

1. [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. [2] D. Cruz-Uribe, A. Fiorenza,Variable Lebesgue Spaces. Birkhuser, Basel, 2013.
3. [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. [4] K.P. Ho, Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces,Sci. China Math.60 (2017), 449-468.
5. [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. [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. [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. [8] L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponent, Lecture Notes in Mathematics, 2017 (2011), Springer.

9. [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. [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. [11] Y. Sawano, S. Sugano, H. Tanaka, Orlicz-Morrey spaces and fractional operators, Potential Anal. 36 (2012), 517-556.