This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class,if and only if Hardy-Littlewood maximal function M is bounded from ...This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class,if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L^p(ω) to weighted Morrey spaces M_q^p(ω) for 1<q<p<∞. As a corollary,if M is(weak) bounded on M_q^p(ω),then ω∈A_p. The A_p condition also characterizes the boundedness of the Riesz transform R_j and convolution operators T_e on weighted Morrey spaces. Finally,we show that ω∈A_p if and only if ω∈ BMO^(p′)(ω) for 1≤p<∞ and 1/p+1/p′= 1.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11661075)
文摘This manuscript addresses Muckenhoupt A_p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A_p class,if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L^p(ω) to weighted Morrey spaces M_q^p(ω) for 1<q<p<∞. As a corollary,if M is(weak) bounded on M_q^p(ω),then ω∈A_p. The A_p condition also characterizes the boundedness of the Riesz transform R_j and convolution operators T_e on weighted Morrey spaces. Finally,we show that ω∈A_p if and only if ω∈ BMO^(p′)(ω) for 1≤p<∞ and 1/p+1/p′= 1.
