Related papers: Sharp embeddings between weighted Paley-Wiener spa…
Using the technique of Gabor analysis, an equivalent characterization is established for the boundedness $e^{i\Delta}: W^{p,q}_m\rightarrow W^{p,q}$, where $0<p_i,q_i\leq\infty$ and $m$ is a $v$-moderate weight. The sharp exponents for the…
We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are…
We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises…
We derive bilateral estimates for the constants appearing in the Fourier transform restricted theorems on the Euclidean sphere for the ordinary and especially radial functions belonging to the Lebesgue-Riesz spaces as well as belonging to…
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space $\dot W^{1,p}$. The resulting spaces are identified as a special class of real interpolation spaces of…
We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…
We prove a lower bound on the sharp Poincar\'e-Sobolev embedding constants for general open sets, in terms of their inradius. We consider the following two situations: planar sets with given topology; open sets in any dimension, under the…
When studying the weighted Hardy-Rellich inequality in $L^2$ with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in the first situation. Our contribution is to determine the new…
In this paper we first study the generalized weighted Hardy spaces $H^p_{L,w}(X)$ for $0<p\le 1$ associated to nonnegative self-adjoint operators $L$ satisfying Gaussian upper bounds on the space of homogeneous type $X$ in both cases of…
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By…
We establish boundedness results for bilinear singular integral operators with rough homogeneous kernels whose restriction to the unit sphere belongs to the Orlicz space $L(\log L)^\alpha$. This improves the previously best known condition…
The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with…
The paper is concerned with sharp estimates of constants in Poincare type inequalities for functions having zero mean value on the boundary of a Lipschitz domain or on a measurable part of it. These estimates are useful for various…
This paper establishes several sharp spectral results for analytic quasiperiodic Schrodinger operators. Key contributions include: (1) exact exponential decay rates for spectral gaps of the almost Mathieu operator, addressing a question…
By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on $\T$. More can be said if the spectrum of the associated inner function has holes…
The paper deals with trace operators of Wiener amalgam spaces using frequency-uniform decomposition operators and maximal inequalities, obtaining sharp results. Additionally, we provide the embeddings between standard and anisotropic Wiener…
We study the sharp constant in the embedding theorem $H^1(0,2\pi)\to L_q(0,2\pi)$ in the case where the norm in $H^1(0,2\pi)$ is defined via the energy of a 1D magnetic Schr\"odinger operator.
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
We observe $(X_i,Y_i)_{i=1}^n$ where the $Y_i$'s are real valued outputs and the $X_i$'s are $m\times T$ matrices. We observe a new entry $X$ and we want to predict the output $Y$ associated with it. We focus on the high-dimensional…