Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu; Yue Ping Zhu

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 4, page 969-987
  • ISSN: 0011-4642

Abstract

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We introduce a new type of variable exponent function spaces M K ˙ q , p ( · ) α ( · ) , λ ( ℝ n ) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators of BMO function on these Morrey-Herz type spaces by applying the properties of variable exponent and BMO norms.

How to cite

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Lu, Yan, and Zhu, Yue Ping. "Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents." Czechoslovak Mathematical Journal 64.4 (2014): 969-987. <http://eudml.org/doc/269837>.

@article{Lu2014,
abstract = {We introduce a new type of variable exponent function spaces $M\dot\{K\}^\{\alpha (\cdot ),\lambda \}_\{q,p(\cdot )\}(\mathbb \{R\}^n)$ of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents $\alpha $ and $p$ are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators of BMO function on these Morrey-Herz type spaces by applying the properties of variable exponent and BMO norms.},
author = {Lu, Yan, Zhu, Yue Ping},
journal = {Czechoslovak Mathematical Journal},
keywords = {Morrey-Herz space; variable exponent; sublinear operator; commutator; Morrey-Herz space; variable exponent; sublinear operator; commutator},
language = {eng},
number = {4},
pages = {969-987},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents},
url = {http://eudml.org/doc/269837},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Lu, Yan
AU - Zhu, Yue Ping
TI - Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 969
EP - 987
AB - We introduce a new type of variable exponent function spaces $M\dot{K}^{\alpha (\cdot ),\lambda }_{q,p(\cdot )}(\mathbb {R}^n)$ of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents $\alpha $ and $p$ are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators of BMO function on these Morrey-Herz type spaces by applying the properties of variable exponent and BMO norms.
LA - eng
KW - Morrey-Herz space; variable exponent; sublinear operator; commutator; Morrey-Herz space; variable exponent; sublinear operator; commutator
UR - http://eudml.org/doc/269837
ER -

References

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