scholarly journals A Vector-Valued Sharp Maximal Inequality on Morrey Spaces with Non-Doubling Measures

2006 ◽  
Vol 13 (1) ◽  
pp. 153-172 ◽  
Author(s):  
Yoshihiro Sawano
Keyword(s):  
Growth Condition ◽  
Maximal Inequality ◽  
Morrey Spaces ◽  
Vector Valued ◽  
Doubling Measures

Abstract We consider the vector-valued extension of the Fefferman–Stein–Strömberg sharp maximal inequality under growth condition. As an application we obtain a vector-valued extension of the boundedness of the commutator. Furthermore, we prove the boundedness of the commutator.

Compact Commutators on Morrey Spaces with Non-Doubling Measures

2008 ◽  
Vol 15 (2) ◽  
pp. 353-376
Author(s):  
Yoshihiro Sawano ◽  
Satoru Shirai
Keyword(s):  
Growth Condition ◽  
Singular Integral ◽  
Radon Measure ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Smooth Functions ◽  
Fractional Integral Operators ◽  
Bmo Functions ◽  
Doubling Measures

Abstract We study multi-commutators on the Morrey spaces generated by BMO functions and singular integral operators or by BMO functions and fractional integral operators. We place ourselves in the setting of coming with a Radon measure μ which satisfies a certain growth condition. The Morrey-boundedness of commutators is established by M. Yan and D. Yang. However, the corresponding assertion of Morrey-compactness is still missing. The aim of this paper is to prove that the multi-commutators are compact if one of the BMO functions can be approximated with compactly supported smooth functions.

scholarly journals Embedding of vector-valued Morrey spaces and separable differential operators

2019 ◽  
Vol 09 (02) ◽  
pp. 1950013 ◽  
Author(s):  
Maria Alessandra Ragusa ◽  
Veli Shakhmurov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Operators ◽  
Maximal Regularity ◽  
Elliptic Partial Differential Equations ◽  
Morrey Spaces ◽  
Embedding Theorems ◽  
Partial Differential ◽  
Infinite Systems ◽  
Vector Valued

The paper is the first part of a program devoted to the study of the behavior of operator-valued multipliers in Morrey spaces. Embedding theorems and uniform separability properties involving [Formula: see text]-valued Morrey spaces are proved. As a consequence, maximal regularity for solutions of infinite systems of anisotropic elliptic partial differential equations are established.

scholarly journals Endpoint estimates for homogeneous Littlewood-Paleyg-functions with non-doubling measures

2009 ◽  
Vol 7 (2) ◽  
pp. 187-207 ◽  
Author(s):  
Dachun Yang ◽  
Dongyong Yang
Keyword(s):  
Hardy Space ◽  
Growth Condition ◽  
Radon Measure ◽  
Open Ball ◽  
Almost Everywhere ◽  
Doubling Measures

Letµbe a nonnegative Radon measure on ℝdwhich satisfies the growth condition that there exist constantsC0> 0 andn∈ (0, d] such that for allx∈ ℝdand r > 0,μ(B(x,r))≤C0rn, whereB(x, r) is the open ball centered atxand having radiusr. In this paper, when ℝdis not an initial cube which impliesµ(ℝd) = ∞, the authors prove that the homogeneous Littlewood-Paleyg-function of Tolsa is bounded from the Hardy spaceH1(µ) toL1(µ), and furthermore, that iff∈ RBMO (µ), then [ġ(f)]2is either infinite everywhere or finite almost everywhere, and in the latter case, [ġ(f)]2belongs to RBLO (µ) with norm no more thanC‖f‖RBMO(μ)2, whereC≻0is independent off.

Multi-Morrey spaces for non-doubling measures

2019 ◽  
Vol 69 (4) ◽  
pp. 1039-1052
Author(s):  
Suixin He
Keyword(s):  
Morrey Spaces ◽  
Doubling Measures

scholarly journals Predual Spaces of Morrey Spaces with Non-doubling Measures

2009 ◽  
Vol 32 (2) ◽  
pp. 471-486 ◽  
Author(s):  
Yoshihiro SAWANO ◽  
Hitoshi TANAKA
Keyword(s):  
Morrey Spaces ◽  
Doubling Measures
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