A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone ...A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W（hp, e∞） to W（Lp,e∞）. This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W（L1, e∞） velong to L1.展开更多
Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtd...Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtds on modulation spaces, where Q^2 = [0, 1] × [0, 1] is the unit square in two dimensions.展开更多
基金Supported by the Hungarian Scientific Research Funds (OTKA) No. K67642
文摘A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W（hp, e∞） to W（Lp,e∞）. This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W（L1, e∞） velong to L1.
基金Supported by NNSF(Grant Nos.11201003 and 11771223)University NSR Project of Anhui Province(Grant Nos.KJ2017ZD27 and KJ2015A117)
文摘Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtds on modulation spaces, where Q^2 = [0, 1] × [0, 1] is the unit square in two dimensions.
