Estimates for Fractional Integral Operators and Linear Commutators on Certain Weighted Amalgam Spaces. (3rd August 2020)

• Record Type: Journal Article
• Authors: Wang, Hua
• Other Names: Zhu Kehe Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-08-03
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/2697104
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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 I γ on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators b, I γ generated by b and I γ are established as well. In addition, we are going to study related problems about two-weight, weak-type inequalities for I γ and b, I γ 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 M γ 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 L 2 R n with Gaussian kernel bounds.