Related papers: On a theorem of Mattila in the p-adic setting

In this paper we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic $p$-Laplacian. The critical exponent is the usual $p^{\star}$ such that the embedding…

We introduce some (p,q)-deformations of the weight multiplicities for the representations of any simple Lie algebra g over the complex numbers. This is done by associating the indeterminate q to the positive roots of a parabolic subsystem…

It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB approach to account for coupling of arbitrary strength by…

We introduce the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions and establish new results which complement and extend the theorems obtained in [BoFW] and [A]. Here is a sample of…

Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…

We study positive properties of the quasilinear elliptic equation $$-\mathrm{div}\mathcal{A}(x,\nabla u)+V|u|^{p-2}u=0\quad (1<p<\infty)\qquad \mbox{ in } \Omega,$$ where the function $\mathcal{A}(x,\xi)$ is induced by a family of norms on…

In this paper, by establishing a Borel-Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random…

H. Landau's necessary density conditions for sampling and interpolation may be viewed as a general principle resting on a basic fact of Fourier analysis: The complex exponentials $e^{i kx}$ ($k$ in $\mathbb{Z}$) constitute an orthogonal…

We extend two well-known results in additive number theory, S\'ark\"ozy's theorem on square differences in dense sets and a theorem of Green on long arithmetic progressions in sumsets, to subsets of random sets of asymptotic density 0. Our…

In this contribution, we are interested in the analysis of a semi-implicit time discretization scheme for the approximation of a parabolic equation driven by multiplicative colored noise involving a $p$-Laplace operator (with $p\geq 2$),…

Let $F$ be a field of characteristic $p>2$ and $A\subset F$ have sufficiently small cardinality in terms of $p$. We improve the state of the art of a variety of sum-product type inequalities. In particular, we prove that $$ |AA|^2|A+A|^3…

The paper studies compactness properties of the affine Sobolev inequality of Gaoyong Zhang et al in the case $p=2$, and existence and regularity of related minimizers, in particular, solutions to the nonlocal Dirichlet problems \[…

For a finite set $A\subset \mathbb{R}$ and real $\lambda$, let $A+\lambda A:=\{a+\lambda b :\, a,b\in A\}$. Combining a structural theorem of Freiman on sets with small doubling constants together with a discrete analogue of…

We establish upper bounds on the size of the largest subset of $\{1,2,\dots,N\}$ lacking nonzero differences of the form $h(p_1,\dots,p_{\ell})$, where $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ is a fixed polynomial satisfying appropriate…

We prove that, given $2<p<\infty$, the Fourier coefficients of functions in $L_2(\mathbb{T}, \lvert t \rvert^{1-2/p}\, dt)$ belong to $\ell_p$, and that, given $1<p<2$, the Fourier series of sequences in $\ell_p$ belong $L_2(\mathbb{T},…

For a fixed rational number g and integers a and d the sets N_g(a,d), respectively R_g(a,d), of primes p for which the order, respectively the index of g(mod p) is congruent to a(mod d), are considered. Under the Generalized Riemann…

We develop a theory of generalized solutions of the nonlinear evolution equations for complex-valued functions of a real positive time variable and $p$-adic spatial variable, which can be seen as non-Archimedean counterparts of the…

By making use of arithmetic information inequalities, we give a strong quantitative bound for the discretised ring theorem. In particular, we show that if $A \subset [1,2]$ is a $(\delta,\sigma)$-set, with $|A| = \delta^{-\sigma},$ then…

Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every…

We investigate the well-posedness in the generalized Hartree equation $iu_t + \Delta u + (|x|^{-(N-\gamma)} \ast |u|^p)|u|^{p-2}u=0$, $x \in \mathbb{R}^N$, $0<\gamma<N$, for low powers of nonlinearity, $p<2$. We establish the local…