Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

Ka Luen Cheung; Kwok-Pun Ho

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 1, page 159-171
  • ISSN: 0011-4642

Abstract

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The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.

How to cite

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Cheung, Ka Luen, and Ho, Kwok-Pun. "Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent." Czechoslovak Mathematical Journal 64.1 (2014): 159-171. <http://eudml.org/doc/261983>.

@article{Cheung2014,
abstract = {The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.},
author = {Cheung, Ka Luen, Ho, Kwok-Pun},
journal = {Czechoslovak Mathematical Journal},
keywords = {block space; variable exponent analysis; Hardy-Littlewood maximal operator; block space; variable exponent analysis; Hardy-Littlewood maximal operator},
language = {eng},
number = {1},
pages = {159-171},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent},
url = {http://eudml.org/doc/261983},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Cheung, Ka Luen
AU - Ho, Kwok-Pun
TI - Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 159
EP - 171
AB - The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.
LA - eng
KW - block space; variable exponent analysis; Hardy-Littlewood maximal operator; block space; variable exponent analysis; Hardy-Littlewood maximal operator
UR - http://eudml.org/doc/261983
ER -

References

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