scholarly journals Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces

2013 ◽  
Vol 29 (1) ◽  
pp. 72-85 ◽  
Author(s):  
H. Wang
Keyword(s):  
Morrey Spaces ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Weighted Morrey Spaces ◽  
Kernel Bounds

scholarly journals Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiheng Wang ◽  
Zengyan Si
Keyword(s):  
Analytic Semigroup ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Locally Integrable Function ◽  
Kernel Bounds ◽  
Necessary And Sufficient

LetLbe the infinitesimal generator of an analytic semigroup onL2(Rn)with Gaussian kernel bounds, and letL-α/2be the fractional integrals ofLfor0<α<n. For any locally integrable functionb, the commutators associated withL-α/2are defined by[b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). Whenb∈BMO(ω)(weightedBMOspace) orb∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of[b,L-α/2]on weighted Morrey spaces, respectively.

scholarly journals Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Sha He ◽  
Taotao Zheng ◽  
Xiangxing Tao
Keyword(s):  
Morrey Spaces ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Bmo Space ◽  
Laplacian Operator ◽  
Fractional Integral Operators ◽  
Weighted Bmo ◽  
Weighted Morrey Spaces ◽  
Integrable Functions ◽  
Multilinear Commutators

LetLbe the infinitesimal generator of an analytic semigroup onL2(Rn)with Gaussian kernel bounds, and letL-α/2be the fractional integrals ofLfor0<α<n. Assume thatb→=(b1,b2,…,bm)is a finite family of locally integrable functions; then the multilinear commutators generated byb→andL-α/2are defined byLb→-α/2f=[bm,…,[b2,[b1,L-α/2]],…]f. Assume thatbjbelongs to weighted BMO space,j=1,2,…,m; the authors obtain the boundedness ofLb→-α/2on weighted Morrey spaces. As a special case, whenL=-Δis the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutatorIαb→on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.

scholarly journals Estimates for Fractional Integral Operators and Linear Commutators on Certain Weighted Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-25 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Strong Type ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Kernel Bounds ◽  
Amalgam Spaces

In this paper, we first introduce some new classes of weighted amalgam spaces. Then, we give the weighted strong-type and weak-type estimates for fractional integral operators Iγ on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators b,Iγ generated by b and Iγ are established as well. In addition, we are going to study related problems about two-weight, weak-type inequalities for Iγ and b,Iγ on the weighted amalgam spaces and give some results. Based on these results and pointwise domination, we can prove norm inequalities involving fractional maximal operator Mγ and generalized fractional integrals ℒ−γ/2 in the context of weighted amalgam spaces, where 0<γ<n and L is the infinitesimal generator of an analytic semigroup on L2Rn with Gaussian kernel bounds.

scholarly journals Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Wang ◽  
Wentan Yi
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Multiple Weights ◽  
Multilinear Fractional Integrals

We will study the boundedness properties of multilinear Calderón-Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

scholarly journals Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Hua Wang
Keyword(s):  
Schrödinger Operator ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Laplacian Operator ◽  
Schrodinger Operator ◽  
Reverse Hölder Class ◽  
Hölder Class ◽  
Weighted Morrey Spaces ◽  
Holder Class ◽  
Reverse Hölder

Let ℒ=−Δ+V be a Schrödinger operator on ℝd, d≥3, where Δ is the Laplacian operator on ℝd, and the nonnegative potential V belongs to the reverse Hölder class RHs with s≥d/2. For given 0<α<d, the fractional integrals associated with the Schrödinger operator ℒ is defined by ℐα=ℒ−α/2. Suppose that b is a locally integrable function on ℝd and the commutator generated by b and ℐα is defined by b.ℐαfx=bx⋅ℐαfx−ℐαbfx. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHs with s≥d/2. Then, we will establish the boundedness properties of the fractional integrals ℐα on these new spaces. Furthermore, weighted strong-type estimate for the corresponding commutator b,ℐα in the framework of Morrey space is also obtained. The classes of weights, the classes of symbol functions, as well as weighted Morrey spaces discussed in this paper are larger than Ap,q, BMOℝd, and Lp,κμ,ν corresponding to the classical case (that is V≡0).

scholarly journals Rough Multilinear Fractional Integrals on Weighted Morrey Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiao Li ◽  
Runqing Cui
Keyword(s):  
Morrey Spaces ◽  
Higher Order ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Rough Kernels ◽  
Weighted Morrey Spaces ◽  
Multilinear Fractional Integrals ◽  
Multilinear Fractional Operators

It is showed that a class of multilinear fractional operators with rough kernels, which are similar to the higher-order commutators for the rough fractional integrals, are bounded on the weighted Morrey spaces.

scholarly journals Operators with Gaussian kernel bounds on mixed Morrey spaces

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5219-5230 ◽  
Author(s):  
Francesca Anceschi ◽  
Christopher Goodrich ◽  
Andrea Scapellato
Keyword(s):  
Analytic Semigroup ◽  
Morrey Spaces ◽  
Gaussian Kernel ◽  
Fractional Operator ◽  
Lipschitz Spaces ◽  
Kernel Bounds

Let L be an analytic semigroup on L2(Rn) with Gaussian kernel bound, and let L-?/2 be the fractional operator associated to L for 0 < ? < n. In this paper, we prove some boundedness properties for the commutator [b,L-?/2] on Mixed Morrey spaces Lq,? (0,T,Lp,?(Rn)), when b belongs to BMO(Rn) or to suitable homogeneous Lipschitz spaces.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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