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 Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Bijun Ren ◽  
Enbin Zhang
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Linear Operators ◽  
Identity Operator ◽  
Zygmund Operator ◽  
Weighted Bmo ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Bmo Spaces ◽  
Toeplitz Type Operator

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

scholarly journals Estimates of Some Operators on One-Sided Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Shaoguang Shi ◽  
Zunwei Fu
Keyword(s):  
Harmonic Analysis ◽  
Fractional Integral ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces

A version of one-sided weighted Morrey space is introduced. The boundedness of some classical one-sided operators in harmonic analysis and PDE on these spaces are discussed, including the Riemann-Liouville fractional integral.

scholarly journals Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 49-61
Author(s):  
Vagif S. Guliyev ◽  
Mehriban N. Omarova
Keyword(s):  
Morrey Space ◽  
Discontinuous Coefficients ◽  
Morrey Spaces ◽  
Oblique Derivative Problem ◽  
Derivative Problem ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Vmo Coefficients ◽  
Generalized Weighted Morrey Space ◽  
The Right

AbstractWe obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space $\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.

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 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.

Sign in / Sign up

Export Citation Format

Share Document