Related papers: Lower bounds for the Wiener norm in $\mathbb{Z}_p^…

The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…

We estimate in Lp the maximal Riesz transform in terms of the Riesz transform itself for p greater than 1. In the limiting case p=1 the weak L1 inequality is shown to fail. Surprisingly, the weak L1 inequality for the maximal Beurling…

We shall consider a result of Fel'dman, where a sharp Baker-type lower bound is obtained for linear forms in the values of some E-functions. Fel'dman's proof is based on an explicit construction of Pad\'e approximations of the first kind…

This paper addresses the problem of deciding the lower-boundedness of an arbitrary real polynomial p in n variables.

The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible…

We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.

We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi(x)=\phi(|x_1|, \dots, |x_m|)$, $x_i\in \mathbf R^{n_i}$, in terms of the Fourier transform of the function $\phi$ on $\mathbf…

This paper describes a method to compute lower bounds for moments of $\zeta$ and $L$-functions. The method is illustrated in the case of moments of $|\zeta(\frac 12+it)|$, where the results are new for small moments $0< k<1$.

We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This…

In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…

We give a general lower bound on the frequency of sign changes in the real coefficients of L-functions of the Selberg class. We in particular recover existing results in the cases of GL(2) and GL(3), and obtain new bounds in the case of…

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…

We derive sharp lower bounds for L^p-functions on the n-dimensional unit hypercube in terms of their p-th marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the…

In this paper we obtain the $L^p$-boundedness of Riesz transforms for Dunkl transform for all $1<p<\infty$.

In this paper we prove weighted norm inequalities for Weyl multipliers satisfying Mauceri's condition. As applications of this we obtain some estimates for $L^p$ multipliers on the Heisenberg group and also show in the context of a theorem…

This paper investigates the relation between the Fourier transform of {\rm BV} (bounded variation) functions and their jump sets. We introduce the notion of $L^2$-jump product and obtain a weighted Plancherel identity for {\rm BV}…

In this paper we continue the study of the spectral gap of Schr\"odinger operators on large intervals and subject to Neumann boundary conditions. The main goal is to derive a lower bound on the spectral gap which is polynomial in the…

We generalize the well-known inequality that the limit of the $L^p$ norm of a function as $p\rightarrow\infty$ is the $L^\infty$ norm to the scale of Orlicz spaces.

We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvment of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin type estimates of…

We provide a new version of the Wiener-Ikehara theorem where one deduces bounds $$ 0< \liminf_{x\to\infty} \frac{S(x)}{e^{x}}\leq \limsup_{x\to\infty} \frac{S(x)}{e^{x}} <\infty $$ for (in particular) a non-decreasing function $S$ from a…