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- W2555732409 abstract "This manuscript addresses Muckenhoupt $A_{p}$ weight theory in connection to Morrey and BMO spaces. It is proved that $omega$ belongs to Muckenhoupt $A_{p}$ class, if and only if Hardy-Littlewood maximal function $M$ is bounded from weighted Lebesgue spaces $L^{p}(omega)$ to weighted Morrey spaces $M^{p}_{q}(omega)$ for $1<q< p<infty$. As a corollary, if $M$ is (weak) bounded on $M^{p}_{q}(omega)$, then $omegain A_{p}$. The $A_{p}$ condition also characterizes the boundedness of the Riesz transform $R_{j}$ and convolution operators $T_{epsilon}$ on weighted Morrey spaces. Finally, we show that $omegain A_{p}$ if and only if $omegain mathrm{BMO}^{p'}(omega)$ for $1leq p< infty$ and $1/p+1/p'=1$." @default.
- W2555732409 created "2016-11-30" @default.
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- W2555732409 date "2016-11-18" @default.
- W2555732409 modified "2023-09-25" @default.
- W2555732409 title "Another characterizations of Muckenhoupt $A_{p}$ class" @default.
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