It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space to (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type . As a consequence we show that the dyadic integral of a ∞ function is dyadically differentiable and its derivative is f a.e.
This paper obtains a class of tight framelet packets on from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.
The aim of this paper is to prove a quantitative version of Shapiro's uncertainty principle for orthonormal sequences in the setting of Gabor-Hankel theory.
The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet...