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Full-Text Articles in Physical Sciences and Mathematics
Commutators In The Two-Weight Setting, Irina Holmes, Michael T. Lacey, Brett D. Wick
Commutators In The Two-Weight Setting, Irina Holmes, Michael T. Lacey, Brett D. Wick
Mathematics Faculty Publications
Let R be the vector of Riesz transforms on Rn and let μ,λ∈Ap be two weights on Rn, 1p(μ)→Lp(λ)|| is shown to be equivalent to the function b being in a BMO space adapted to μ and λ. This is a common extension of a result of Coifman–Rochberg–Weiss in the case of both λ and μ being Lebesgue measure, and Bloom in the case of dimension one.
Unions Of Lebesgue Spaces And A1 Majorants, Greg Knese, John E. Mccarthy, Kabe Moen
Unions Of Lebesgue Spaces And A1 Majorants, Greg Knese, John E. Mccarthy, Kabe Moen
Mathematics Faculty Publications
We study two questions. When does a function belong to the union of Lebesgue spaces, and when does a function have an A1 majorant? We provide a systematic study of these questions and show that they are fundamentally related. We show that the union ofLwp(ℝn)spaces withw∈Apis equal to the union of all Banach function spaces for which the Hardy–Littlewood maximal function is bounded on the space itself and its associate space.