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