Related papers: A transference result for Lebesgue spaces with $A_…
In this paper we improve and complement a result by M\'oricz and Siddiqi \cite{Mor}. In particular, we prove that their inequality of the N\"orlund means with respect to the Walsh system holds also without their additional condition.…
Some results of microlocal continuity for pseudodifferential operators whose non regular symbols belong to weighted Fourier Lebesgue spaces are given. Inhomogeneous local and microlocal propagation of singularities of Fourier Lebesgue type…
We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko's framework for polynomial space computability in $\mathbb{R}^n$ to define…
In this article we obtain an "off-diagonal" version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12]…
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration…
We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to…
Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…
In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal functions, potentials and Calder\'on-Zygmund singular integrals in variable exponent Lebesgue spaces defined on quasimetric measure spaces $(X,…
We study the problem estimation of classical Lebesgue-Riesz and Grand Lebesgue Norm for the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces as well as from the modified Besov's spaces.
In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is…
In this paper we obtain the non-asymptotic norm estimations of Besov's type between the norms of a functions in different Bilateral Grand Lebesgue spaces (BGLS). We also give some examples to show the sharpness of these inequalities.
A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given that applies to the various Hardy operators and their duals,…
In this article, one investigates in a very general frame mass transference principles from ball to arbitrary open sets when the sequence of balls is distributed according to a finite measure. As an application of the main theorem, a mass…
In this short article we obtain the non-asymptotic upper and low estimations for linear and bilinear weight Riesz's functional through the Lebesgue spaces.
We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We…
We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. Especially we recover some known results.
We obtain results concerning the so-called factorization for the convergence of random variables almost everywhere (almost surely or with probability one), belonging to the classical Lebesgue-Riesz spaces and we extend these results to the…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
For each $f\in L^p({\mathbb R)}$ ($1\leq p<\infty$) it is shown that the Fourier transform is the distributional derivative of a H\"older continuous function. For each $p$ a norm is defined so that the space Fourier transforms is…
In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…