Article ID Journal Published Year Pages File Type
8904466 Acta Mathematica Scientia 2017 14 Pages PDF
Abstract
This manuscript addresses Muckenhoupt Ap weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces Lp(ω) to weighted Morrey spaces Mqp(ω) for 1 < q < p < ∞. As a corollary, if M is (weak) bounded on Mqp(ω), then ω ∈ Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tɛ on weighted Morrey spaces. Finally, we show that ω ∈ Ap if and only if ω∈BMOp′(ω) for 1 ≤ p < ∞ and 1/p+1/p′=1.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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