Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces

Gladis Pradolini; Jorgelina Recchi

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 77-94
  • ISSN: 0011-4642

Abstract

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Let μ be a nonnegative Borel measure on ℝ d satisfying that μ ( Q ) ≤ l ( Q ) n for every cube Q ⊂ ℝ n , where l ( Q ) is the side length of the cube Q and 0 < n ≤ d . We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function B in the context of non-homogeneous spaces related to the measure μ . Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W. Wang, C. Tan, Z. Lou (2012).

How to cite

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Pradolini, Gladis, and Recchi, Jorgelina. "Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces." Czechoslovak Mathematical Journal 68.1 (2018): 77-94. <http://eudml.org/doc/294727>.

@article{Pradolini2018,
abstract = {Let $\mu $ be a nonnegative Borel measure on $\mathbb \{R\}^d$ satisfying that $\mu (Q)\le l(Q)^n$ for every cube $Q\subset \mathbb \{R\}^n$, where $l(Q)$ is the side length of the cube $Q$ and $0<n\le d$. We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function $B$ in the context of non-homogeneous spaces related to the measure $\mu $. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W. Wang, C. Tan, Z. Lou (2012).},
author = {Pradolini, Gladis, Recchi, Jorgelina},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-homogeneous space; generalized fractional operator; weight},
language = {eng},
number = {1},
pages = {77-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces},
url = {http://eudml.org/doc/294727},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Pradolini, Gladis
AU - Recchi, Jorgelina
TI - Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 77
EP - 94
AB - Let $\mu $ be a nonnegative Borel measure on $\mathbb {R}^d$ satisfying that $\mu (Q)\le l(Q)^n$ for every cube $Q\subset \mathbb {R}^n$, where $l(Q)$ is the side length of the cube $Q$ and $0<n\le d$. We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function $B$ in the context of non-homogeneous spaces related to the measure $\mu $. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W. Wang, C. Tan, Z. Lou (2012).
LA - eng
KW - non-homogeneous space; generalized fractional operator; weight
UR - http://eudml.org/doc/294727
ER -

References

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