scholarly journals Integrability properties of integral transforms via morrey spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1274-1299
Author(s):  
Natasha Samko
Keyword(s):  
Morrey Space ◽  
Integral Transforms ◽  
Morrey Spaces ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Weighted Morrey Space ◽  
Multidimensional Integral

Abstract We show that integrability properties of integral transforms with kernel depending on the product of arguments (which include in particular, popular Laplace, Hankel, Mittag-Leffler transforms and various others) are better described in terms of Morrey spaces than in terms of Lebesgue spaces. Mapping properties of integral transforms of such a type in Lebesgue spaces, including weight setting, are known. We discover that local weighted Morrey and complementary Morrey spaces are very appropriate spaces for describing integrability properties of such transforms. More precisely, we show that under certain natural assumptions on the kernel, transforms under consideration act from local weighted Morrey space to a weighted complementary Morrey space and vice versa, where an interplay between behavior of functions and their transforms at the origin and infinity is transparent. In case of multidimensional integral transforms, for this goal we introduce and use anisotropic mixed norm Morrey and complementary Morrey spaces.

On mixed norm Bergman–Orlicz–Morrey spaces

2018 ◽  
Vol 25 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Alexey N. Karapetyants ◽  
Stefan G. Samko
Keyword(s):  
Unit Disc ◽  
Fourier Coefficients ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bergman Projection ◽  
Mixed Norm ◽  
Taylor Coefficients ◽  
Type Spaces ◽  
Radial Variable

Abstract Following the ideas of our previous research, in this paper we continue the study of new Bergman-type spaces on the unit disc with mixed norm in terms of Fourier coefficients. Here we deal with the case where the sequence of norms of Fourier coefficients in the Orlicz–Morrey space in radial variable belongs to {l^{q}} . We study the boundedness of the Bergman projection and provide a description of functions in these spaces via the behavior of their Taylor coefficients.

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 $\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.

Two-Weighted Estimates for Some Integral Transforms in the Lebesgue Spaces with Mixed Norm and Imbedding Theorems

1994 ◽  
Vol 1 (5) ◽  
pp. 495-503
Author(s):  
V. Kokilashvili
Keyword(s):  
Integral Transforms ◽  
Mixed Norm ◽  
Weighted Inequalities ◽  
Lebesgue Spaces ◽  
Weighted Estimates ◽  
Weighted Lebesgue Spaces

Abstract Two-weighted inequalities are proved for anisotropic potentials. These estimates are used to obtain the refinements of the well-known imbedding theorems in the scale of weighted Lebesgue spaces.

scholarly journals Embeddings of weighted generalized Morrey spaces into Lebesgue spaces on fractal sets

2019 ◽  
Vol 22 (5) ◽  
pp. 1203-1224
Author(s):  
Natasha Samko
Keyword(s):  
Morrey Space ◽  
General Setting ◽  
Morrey Spaces ◽  
General Nature ◽  
Sufficient Condition ◽  
Lebesgue Spaces ◽  
Generalized Morrey Spaces ◽  
Fractal Sets ◽  
Measure Spaces ◽  
Logarithmic Type

Abstract We study embeddings of weighted local and consequently global generalized Morrey spaces defined on a quasi-metric measure set (X, d, μ) of general nature which may be unbounded, into Lebesgue spaces Ls(X), 1 ≤ s ≤ p < ∞. The main motivation for obtaining such an embedding is to have an embedding of non-separable Morrey space into a separable space. In the general setting of quasi-metric measure spaces and arbitrary weights we give a sufficient condition for such an embedding. In the case of radial weights related to the center of local Morrey space, we obtain an effective sufficient condition in terms of (fractional in general) upper Ahlfors dimensions of the set X. In the case of radial weights we also obtain necessary conditions for such embeddings of local and global Morrey spaces, with the use of (fractional in general) lower and upper Ahlfors dimensions. In the case of power-logarithmic-type weights we obtain a criterion for such embeddings when these dimensions coincide.

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 Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

Sign in / Sign up

Export Citation Format

Share Document