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.
We propose a cryptographic algorithm utilizing integer wavelet transform via a lifting scheme. In this research, we construct some predict and update operators within the lifting scheme of wavelet transforms employing operations in min-max-plus algebra, termed as lifting scheme integer wavelet transform over min-max-plus algebra (MMPLS-IWavelet). The analysis and synthesis process on MMPLS-IWavelet is implemented for both encryption and decryption processes. The encryption key comprises a sequence...
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.