scholarly journals Boundedness ofθ-Type Calderón–Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Morrey Space ◽  
Weak Type ◽  
Strong Type ◽  
Type Estimate ◽  
Generalized Morrey Space ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Special Cases ◽  
Type Spaces

We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strong-type and weak-type estimates for a class of Calderón–Zygmund type operatorsTθin these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators[b,Tθ]formed bybandTθare established. Also, we study related problems about two-weight, weak-type inequalities forTθand[b,Tθ]in the Morrey type spaces and give partial results.

scholarly journals Vector-Valued Inequalities in the Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Hua Wang
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Doubling Condition ◽  
Littlewood Maximal Function ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued

We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spacesLp,κ(w)when1≤p<∞and0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals Boundedness of Vector-Valued Intrinsic Square Functions in Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Square Functions ◽  
Doubling Condition ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued ◽  
Intrinsic Square Functions

We will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the weighted Morrey spacesLp,κ(w)when1≤p<∞,0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals Estimates of Intrinsic Square Functions on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guilian Gao ◽  
Xiaomei Wu
Keyword(s):  
Weak Type ◽  
Morrey Spaces ◽  
Strong Type ◽  
Square Functions ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Intrinsic Square Functions

We prove the boundedness of the intrinsic functions on generalized weighted Morrey spacesMp,φ(w), including the strong type estimates and weak type estimates. Moreover, we define thekth-order commutators generated byBMORnfunctions and intrinsic functions, and obtain their strong type estimates onMp,φ(w). In some cases, we improve previous results.

scholarly journals Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Hua Wang
Keyword(s):  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Strong Type ◽  
Type Estimate ◽  
Reverse Hölder Class ◽  
Hölder Class ◽  
Weighted Morrey Spaces ◽  
Holder Class ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator, whereΔis the Laplacian onRdand the nonnegative potentialVbelongs to the reverse Hölder classRHqforq≥d. The Riesz transform associated with the operatorL=-Δ+Vis denoted byR=∇(-Δ+V)-1/2and the dual Riesz transform is denoted byR⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder classRHqforq≥d. Then we will establish the mapping properties of the operatorRand its adjointR⁎on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators[b,R]and[b,R⁎]are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger thanAp,BMO(Rd), andLp,κ(w)corresponding to the classical Riesz transforms (V≡0).

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.

Weighted inequalities for some integral operators with rough kernels

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
María Riveros ◽  
Marta Urciuolo
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Degree Zero ◽  
Weighted Inequalities ◽  
Rough Kernels ◽  
Type Estimate ◽  
Dini Condition ◽  
Weighted Bmo ◽  
Weak Type Estimates ◽  
Invertible Matrices

AbstractIn this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.

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 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.

Sign in / Sign up

Export Citation Format

Share Document