Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents

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Abstract

We study the local Morrey spaces with variable exponents. We show that the local block space with variable exponents are pre-duals of the local Morrey spaces with variable exponents. Using this duality, we establish the extrapolation theory for the local Morrey spaces with variable exponents. The extrapolation theory gives the mapping properties for the local sharp maximal functions, the geometric maximal functions and the rough maximal function on the local Morrey spaces with variable exponents. Copyright © 2020 Element d.o.o. publishing house.
Original languageEnglish
Pages (from-to)1509-1528
JournalMathematical Inequalities & Applications
Volume23
Issue number4
DOIs
Publication statusPublished - Oct 2020

Citation

Yee, T.-L., Cheung, K. L., Ho, K.-P., & Suen, C. K. (2020). Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents. Mathematical Inequalities & Applications, 23(4), 1509-1528. doi: 10.7153/mia-2020-23-108

Keywords

  • Variable Lebesgue space
  • Local Morrey space
  • Local block space
  • Extrapolation
  • Local sharp maximal function
  • Geometric maximal function
  • Rough maximal function

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