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.

scholarly journals The Boundedness of the Hardy-Littlewood Maximal Operator and Multilinear Maximal Operator in Weighted Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takeshi Iida
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Type Spaces ◽  
Multilinear Maximal Function ◽  
Multilinear Maximal Operator ◽  
Littlewood Maximal Operator

The aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and multilinear maximal function.

Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces

2021 ◽  
Vol 24 (6) ◽  
pp. 1643-1669
Author(s):  
Natasha Samko
Keyword(s):  
Upper Bound ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Target Space ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Measure Spaces ◽  
Hardy Operators ◽  
Hardy Type Operators

Abstract We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure spaces for a certain class of “radial” weights. Quasi-metric measure spaces may include, in particular, sets of fractional dimentsions. We prove theorems on the boundedness of commutators with CMO coefficients of these operators. Given a domain Morrey space 𝓛 p,φ (X) for the fractional Hardy operators or their commutators, we pay a special attention to the study of the range of the exponent q of the target space 𝓛 q,ψ (X). In particular, in the case of classical Morrey spaces, we provide the upper bound of this range which is greater than the known Adams exponent.

scholarly journals Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 1317-1331
Author(s):  
Vagif Guliyev ◽  
Hatice Armutcu ◽  
Tahir Azeroglu
Keyword(s):  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Necessary And Sufficient Conditions ◽  
Potential Operator ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Potential Operators ◽  
Boundedness Criterion ◽  
Necessary And Sufficient

Abstract In this paper, we give a boundedness criterion for the potential operator { {\mathcal I} }^{\alpha } in the local generalized Morrey space L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the generalized Morrey space {M}_{p,\varphi }(\text{Γ}) defined on Carleson curves \text{Γ} , respectively. For the operator { {\mathcal I} }^{\alpha } , we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the strong and weak Adams-type boundedness on {M}_{p,\varphi }(\text{Γ}) .

Estimates for parabolic equations with measure data in generalized Morrey spaces

2019 ◽  
Vol 21 (05) ◽  
pp. 1850044
Author(s):  
Chao Zhang
Keyword(s):  
Parabolic Equations ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Parabolic Problems ◽  
Measure Data ◽  
Spatial Gradient ◽  
Irregular Domain ◽  
Variable Formula ◽  
Mean Oscillation ◽  
Morrey Estimates

In this paper, we prove the optimal generalized Morrey estimates for the spatial gradient of the solutions obtained by limits of approximations (SOLA) for a class of parabolic problems with right-hand side measure in a very general irregular domain. The nonlinearity is assumed to be merely measurable only in the time variable [Formula: see text] and belongs to the small bounded mean oscillation (BMO) class as functions of the spatial variable [Formula: see text].

scholarly journals On the boundedness of a generalized fractional integral on generalized Morrey spaces

2002 ◽  
Vol 33 (4) ◽  
pp. 335-340
Author(s):  
Eridani Eridani
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Campanato Space ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Generalized Fractional Integral

In this paper we extend Nakai's result on the boundedness of a generalized fractional integral operator from a generalized Morrey space to another generalized Morrey or Campanato space.

Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data

2014 ◽  
Vol 58 (1) ◽  
pp. 199-218 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Lubomira G. Softova
Keyword(s):  
Parabolic Equations ◽  
Regularity Result ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Bmo Functions ◽  
Mean Oscillation ◽  
Sublinear Operators ◽  
Vmo Coefficients ◽  
Morrey Regularity ◽  
Discontinuous Data

AbstractWe prove continuity in generalized parabolic Morrey spacesof sublinear operators generated by the parabolic Calderón—Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. As a consequence, we obtain a global-regularity result for the Cauchy—Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation (VMO) coefficients.

scholarly journals The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

2021 ◽  
Author(s):  
Tair Gadjiev ◽  
Konul Suleymanova
Keyword(s):  
Parabolic Equations ◽  
Unbounded Domains ◽  
Morrey Spaces ◽  
Higher Order ◽  
Bounded Mean Oscillation ◽  
Bmo Functions ◽  
Mean Oscillation ◽  
Sublinear Operators ◽  
Vmo Coefficients ◽  
Discontinuous Data

We study the regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations of higher order with vanishing mean oscillation (VMO) coefficients. We prove continuity in generalized parabolic Morrey spaces Mp,φ of sublinear operators generated by the parabolic Calderon-Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. We obtain strong solution belongs to the generalized Sobolev-Morrey space Wp,φm,1∘Q. Also we consider elliptic equation in unbounded domains.

scholarly journals Parameter θ -Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Guanghui Lu
Keyword(s):  
Measure Space ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Metric Measure Space ◽  
Marcinkiewicz Integral ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Formula Type

Let X , d , μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ -type Marcinkiewicz integral M θ ρ is bounded on the weighted generalized Morrey space L p , ϕ , τ ω for p ∈ 1 , ∞ . Furthermore, the boudedness of M θ ρ on weak weighted generalized Morrey space W L p , ϕ , τ ω is also obtained.

WEIGHTED SOLVABILITY FOR PARABOLIC EQUATIONS WITH PARTIALLY BMO COEFFICIENTS AND ITS APPLICATIONS

2014 ◽  
Vol 96 (3) ◽  
pp. 396-428
Author(s):  
LIN TANG
Keyword(s):  
Bounded Domain ◽  
Parabolic Equations ◽  
Global Regularity ◽  
Morrey Spaces ◽  
Divergence Form ◽  
Bounded Mean Oscillation ◽  
Nondivergence Form ◽  
Mean Oscillation ◽  
Bmo Coefficients

AbstractWe consider the weighted $L_p$ solvability for divergence and nondivergence form parabolic equations with partially bounded mean oscillation (BMO) coefficients and certain positive potentials. As an application, global regularity in Morrey spaces for divergence form parabolic operators with partially BMO coefficients on a bounded domain is established.

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