Norm Inequalities in Generalized Morrey Spaces

Abstract and Applied Analysis

2020

Let Tα0≤α<n be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let b,Tα0≤α<n be the commutators generated by BMORn functions and Tα. This paper is concerned with two-weight, weak-type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criteria for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces.

Section: Introduction and Main Resultsmentioning

confidence: 99%

Two-Weight, Weak-Type Norm Inequalities for a Class of Sublinear Operators on Weighted Morrey and Amalgam Spaces

Abstract and Applied Analysis

2020

“…In order to prove the results for commutators, we need the following properties of BMO . For , and , we get and for all balls B , For all nonnegative integers k , we obtain where , (see [ 4 ]).…”

Section: Notations and Preliminariesmentioning

confidence: 99%

“…Feuto proved in [ 4 ] that Calderón-Zygmund singular integral operators, Marcinkiewicz operators, the maximal operators associated to Bochner-Riesz operators and their commutators are bounded on .…”

Section: Introductionmentioning

confidence: 99%

Weighted norm inequalities for multilinear Calderón-Zygmund operators in generalized Morrey spaces

Liu

2017

J Inequal Appl

“…(iii) if p = α and s = ∞, then ðL p , L s Þ α ðR n Þ reduces to the usual Lebesgue space L p ðR n Þ In [14] (see also [15,16]), Feuto considered a weighted version of the amalgam space ðL p , L s Þ α ðwÞ. A nonnegative measurable function w defined on R n is called a weight if it is locally integrable.…”

Section: Introductionmentioning

confidence: 99%

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

Journal of Function Spaces

2020

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.