Abstract
Abstract In the present paper, the authors investigate the two weight, weak-(p, q) type norm inequalities for a class of sublinear operators 𝓣γ and their commutators [b, 𝓣γ] on weighted Morrey and Amalgam spaces. What should be stressed is that we introduce the new BMO type space and our results generalize known results before.
Highlights
As it is well-known, Muckenhoupt [1] characterized the weights ω by means of the Hardy-Littlewood maximal operator M. He showed that M is bounded on Lp(ω) if and only if ω satis ed the so-called Ap condition: there exists a constant C such that for all cube Q, ˆ
≤ C, Muckenhoupt and Wheeden [2] showed that fractional integral operator Iα is bounded from Lp(ω) to Lq(ω) if and only if ω satis ed the so-called Ap,q condition: there exists a constant C such that for all cube Q, ˆ
≤ C, These estimates are of interest on their own and they have relevance to partial di erential equations and quantum mechanics
Summary
As it is well-known, Muckenhoupt [1] characterized the weights ω by means of the Hardy-Littlewood maximal operator M He showed that M is bounded on Lp(ω) if and only if ω satis ed the so-called Ap condition: there exists a constant C such that for all cube Q, ˆ. ≤ C, Muckenhoupt and Wheeden [2] showed that fractional integral operator Iα is bounded from Lp(ω) to Lq(ω) if and only if ω satis ed the so-called Ap,q condition: there exists a constant C such that for all cube Q, Qq/p ω(x)−p /q dx.
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