scholarly journals Pointwise Multipliers on Weak Morrey Spaces

2020 ◽  
Vol 8 (1) ◽  
pp. 363-381
Author(s):  
Ryota Kawasumi ◽  
Eiichi Nakai
Keyword(s):  
Growth Condition ◽  
Lebesgue Space ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Pointwise Multipliers ◽  
Weak Lebesgue Space ◽  
Weak Morrey Spaces

Abstract We consider generalized weak Morrey spaces with variable growth condition on spaces of homogeneous type and characterize the pointwise multipliers from a generalized weak Morrey space to another one. The set of all pointwise multipliers from a weak Lebesgue space to another one is also a weak Lebesgue space. However, we point out that the weak Morrey spaces do not always have this property just as the Morrey spaces not always.

scholarly journals Commutators on Weighted Morrey Spaces on Spaces of Homogeneous Type

2020 ◽  
Vol 8 (1) ◽  
pp. 305-334
Author(s):  
Ruming Gong ◽  
Ji Li ◽  
Elodie Pozzi ◽  
Manasa N. Vempati
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Doubling Measure ◽  
Bmo Space ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces

Abstract In this paper, we study the boundedness and compactness of the commutator of Calderón– Zygmund operators T on spaces of homogeneous type (X, d, µ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space L ω p , k ( X ) L_\omega ^{p,k}\left( X \right) with κ ∈ (0, 1) and ω ∈ Ap (X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure µ.

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

scholarly journals Pointwise Multipliers on Spaces of Homogeneous Type in the Sense of Coifman and Weiss

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanchang Han ◽  
Fanghui Liao ◽  
Zongguang Liu
Keyword(s):  
Orthonormal Basis ◽  
General Setting ◽  
Doubling Measure ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Pointwise Multipliers ◽  
Additional Assumptions

By applying the remarkable orthonormal basis constructed recently by Ausher and Hytönen on spaces of homogeneous type in the sense of Coifman and Weiss, pointwise multipliers of inhomogeneous Besov and Triebel-Lizorkin spaces are obtained. We make no additional assumptions on the quasi-metric or the doubling measure. Hence, the results of this paper extend earlier related results to a more general setting.

scholarly journals Third Version of Weak Orlicz–Morrey Spaces and Its In-clusion Properties

2019 ◽  
Vol 4 (2) ◽  
pp. 257-262
Author(s):  
Al Azhary Masta ◽  
Siti Fatimah ◽  
Muhammad Taqiyuddin
Keyword(s):  
Morrey Space ◽  
Necessary Conditions ◽  
Orlicz Spaces ◽  
Morrey Spaces ◽  
The Third ◽  
Inclusion Relations ◽  
Sufficient And Necessary Conditions ◽  
Weak Morrey Spaces

Orlicz–Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are  three  versions  of  Orlicz–Morrey  spaces.  In  this  article,  we discussed  the  third  version  of  weak  Orlicz–Morrey  space, which is an enlargement of third version of (strong) Orlicz– Morrey space. Similar to its first version and second version, the third version of weak Orlicz-Morrey space is considered as  a  generalization  of  weak  Orlicz  spaces,  weak  Morrey spaces,  and  generalized  weak  Morrey  spaces.  This  study investigated  some  properties  of the third  version of weak Orlicz–Morrey spaces, especially the sufficient and necessary conditions for inclusion relations between two these spaces. One of the keys to get our result is to estimate the quasi- norm of characteristics function of open balls in ℝ.

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