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We consider the question of giving an upper bound for the first nontrivial eigenvalue of the Wentzell-Laplace operator of a domain $\Omega$, involving only geometrical informations. We provide such an upper bound, by generalizing Brock's…
We prove when a Banach ideal of linear operators defined, or characterized, by the transformation of vector-valued sequences is maximal. Known results are recovered as particular cases and new information is obtained. To accomplish this…
We obtain restriction results of K. de Leeuw's type for maximal operators defined through multilinear Fourier multipliers of either strong or weak type acting on weighted Lebesgue spaces. We give some application of our development. In…
Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family…
We use the theory of Auslander Buchweitz approximations to classify certain resolving subcategories containing a semidualizing or a dualizing module. In particular, we show that if the ring has a dualizing module, then the resolving…
We study a.e. convergence on $L^p$, and Lorentz spaces $L^{p,q}$, $p>\tfrac{2d}{d-1}$, for variants of Riesz means at the critical index $d(\tfrac 12-\tfrac 1p)-\tfrac12$. We derive more general results for (quasi-)radial Fourier…
We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…
Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on…
In this paper we represent the $k$-th Riesz transform in the ultraspherical setting as a principal value integral operator for every $k\in \mathbb{N}$. We also measure the speed of convergence of the limit by proving $L^p$-boundedness…
In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a…
Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations…
In harmonic analysis, studies of inequalities of Riesz potential in various function spaces have a very important place. Variable exponent Morrey type spaces and the examines of the boundedness of such operators on these spaces have an…
In this paper, we consider a maximizing problem associated with the Sobolev type embedding on the space of bounded variation. We show that, although the maximizing problem suffers from both of the non-compactness of vanishing and…
In this paper we investigate Lp-boundedness properties for the higher order Riesz transforms associated with Laguerre operators. Also we prove that the k-th Riesz transform is a principal value singular integral operator (modulus a constant…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…
We provide infinitely many solutions of a Dirichlet problem on balls.
We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the…
One of the classical problems concerns the class of analytic functions $f$ on the open unit disk $|z|<1$ which have finite Dirichlet integral $\Delta(1,f)$, where $$\Delta(r,f)=\iint_{|z|<r}|f'(z)|^2 \, dxdy \quad (0<r\leq 1). $$ The class…