Revista Matemática Complutense最新文献

This paper aims to study (A_p) weights in the context of a class of metric measure spaces with exponential volume growth, namely infinite trees with root at infinity equipped with the geodesic distance and flow measures. Our main result is a Muckenhoupt Theorem, which is a characterization of the weights for which a suitable Hardy–Littlewood maximal operator is bounded on the corresponding weighted (L^p) spaces. We emphasise that this result does not require any geometric assumption on the tree or any condition on the flow measure. We also prove a reverse Hölder inequality in the case when the flow measure is locally doubling. We finally show that the logarithm of an (A_p) weight is in BMO and discuss the connection between (A_p) weights and quasisymmetric mappings.

We address a detailed study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals, as well as those arising by the (L^p)-approximation, as (p rightarrow +infty ) of such functionals. Our quest is motivated by the knowledge we have on the analogous integral functionals and aims at establishing a solid groundwork underlying further research in the (L^infty ) context.

This manuscript presents sufficient conditions for dispersiveness of invariant control systems on nilpotent Lie groups. The main theorem shows that a nilpotent control system is dispersive if its drift vector is not a linear combination of the controlled vectors and the Lie brackets among all the vector fields of the system. This condition implies a necessary condition for the existence of a control set. A classification of homogeneous and inhomogeneous nilpotent control systems is presented.

We derive, using a heuristic method, a p-adic mate of bilateral Ramanujan series. It has (among other consequences) Zudilin’s supercongruences for rational Ramanujan series.

Let (G=(V,E)) be an infinite graph. The purpose of this paper is to investigate the nonexistence of global solutions for the following semilinear heat equation

where (Delta ) is an unbounded Laplacian on G, (alpha ) is a positive parameter and (u_0) is a nonnegative and nontrivial initial value. Using on-diagonal lower heat kernel bounds, we prove that the semilinear heat equation admits the blow-up solutions, which is viewed as a discrete analog of that of Fujita (J Fac Sci Univ Tokyo 13:109–124, 1966) and had been generalized to locally finite graphs with bounded Laplacians by Lin and Wu (Calc Var Partial Diff Equ 56(4):22, 2017). In this paper, new techniques have been developed to deal with unbounded graph Laplacians.

We investigate the boundedness of “vertical” Littlewood–Paley–Stein square functions for the nonlocal fractional discrete Laplacian on the lattice (mathbb {Z}), where the underlying graphs are not locally finite. When (qin [2,infty )), we prove the (l^q) boundedness of the square function by exploring the corresponding Markov jump process and applying the martingale inequality. When (qin (1,2]), we consider a modified version of the square function and prove its (l^q) boundedness through a careful in on the generalized carré du champ operator. A counterexample is constructed to show that it is necessary to consider the modified version. Moreover, we extend the study to a class of nonlocal Schrödinger operators for (qin (1,2]).

A (Bbbk )-configuration of type ((d_1,ldots ,d_s)), where (1leqslant d_1< cdots < d_s ) are integers, is a set of points in ({mathbb P}^2) that has a number of algebraic and geometric properties. For example, the graded Betti numbers and Hilbert functions of all (Bbbk )-configurations in ({mathbb P}^2) are determined by the type ((d_1,ldots ,d_s)). However the Waldschmidt constant of a (Bbbk )-configuration in ({mathbb P}^2) of the same type may vary. In this paper, we find that the Waldschmidt constant of a (Bbbk )-configuration in ({mathbb P}^2) of type ((d_1,ldots ,d_s)) with (d_1ge sge 1) is s. Then we deal with the Waldschmidt constants of standard (Bbbk )-configurations in ({mathbb P}^2) of type (a), (a, b), and (a, b, c) with (age 1). In particular, we prove that the Waldschmidt constant of a standard (Bbbk )-configuration in ({mathbb P}^2) of type (1, b, c) with (cge 2b+2) does not depend on c.

Elucidating a connection with nonlinear Fourier analysis (NLFA), we extend a well known algorithm in quantum signal processing (QSP) to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous as a function of the signal.

We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by Muckenhoupt and Wheeden (Indiana Univ. Math. J. 26(5):801–816, 1977) and later in Cruz-Uribe et al. (Int. Math. Res. Not. 30:1849–1871, 2005). We obtain quantitative estimates for these operators in both the scalar and matrix weighted setting using sparse domination techniques. Our results extend those obtained by Cruz-Uribe et al. (Rev. Mat. Iberoam. 37(4):1513–1538, 2021) for singular integrals and maximal operators when (p=1).