二维空间的离散W变换

利用一维离散Walsh变换的性质与结果,定义了二维离散Walsh变换及二维Walsh变换的逻辑卷积,证明了二元W系的完整性,给出二维Walsh变换的基本运算性质及二维Walsh变换下1≤p≤2时的Hausdorff-Young不等式。

A Growth Behavior of SzegöType Operators

We define new integral operators on the Haydy space similar to Szegö projection. We show that these operators map from Hp to H2 for some 1 ≤ p < 2, where the range of p is depending on a growth condition. To prove that, we generalize the Hausdorff-Young Theorem to multi-dimensional case.

(L^p, L^q)-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces

In this paper, we prove the （L^p, L^q）-boundedness of （fractional） Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.

Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces

In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.

A NOTE ON ＂SMALL AMPLITUDE SOLUTIONS OF THE GENERALIZED IMBQ EQUATION＂

Global existence of small amplitude solution and nonlinear scattering result for the Canchy problem of the generalized IMBq equation were considered in the paper titled ＂Small amplitude solutions of the generalized IMBq equation＂ [1]. It is a pity that the authors overlooked the bad behavior of low frequency part of S（t）ψ which causes troubles in L^∞ and H^＊ estimates. In this note, we will present a new proof of global existence under same conditions as in [1] but for space dimension n ≥ 3.