2022/08/02 by Demir, Sakin
#42B20 #42B30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2209.04033
In this research we introduce the Banach space valued Hp spaces with Ap weight, and prove the following results: Let \mathbbA and \mathbbB Banach spaces, and T be a convolution operator mapping \mathbbA-valued functions into \mathbbB-valued functions, i.e., Tf(x)=∫ℝnK(x-y)⋅ f(y) dy, where K is a strongly measurable function defined on ℝn such that ‖K(x)‖_\mathbbB is locally integrable away from the origin. Suppose that w is a positive weight function defined on ℝn, and that i) For some q∈ [1, ∞ ], there exists a positive constant C1 such that ∫ℝn‖Tf(x)‖q_\mathbbBw(x) dx≤ C1∫ℝn‖f(x)‖_\mathbbAq w(x) dx for all f∈ Lq_\mathbbA(ℝn). ii) There exists a positive constant C2 independent of y∈ℝn such that ∫|x|>2|y|‖K(x-y)-K(x)‖_\mathbbB dx