A modular convergence theorem for certain nonlinear integral operators with homogeneous kernel.
A modulus for property (β) of Rolewicz
We define a modulus for the property (β) of Rolewicz and study some useful properties in fixed point theory for nonexpansive mappings. Moreover, we calculate this modulus in spaces for the main measures of noncompactness.
A Morita equivalence for Hilbert C*-modules
We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.
A multidimensional distribution sampling theorem
Using Bochner-Riesz means we get a multidimensional sampling theorem for band-limited functions with polynomial growth, that is, for functions which are the Fourier transform of compactly supported distributions.
A multi-dimensional spectral theory in C*-algebras
A multidimensional Wolff theorem
A multilinear interpolation theorem
A multiplicative embedding inequality in Orlicz--Sobolev spaces.
A multiplicative functional on the commutative topological field
A multiplier characterization of analytic UMD spaces
A multiplier in Besov spaces which is not a multiplier in Lebesgue spaces
A multiplier theorem on weighted Orlicz spaces
A Natural Class of Sequential Banach Spaces
We introduce and study a natural class of variable exponent spaces, which generalizes the classical spaces and c₀. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. Some geometric examples are constructed by using these spaces.
A natural derivative on [0, n] and a binomial Poincaré inequality
We consider probability measures supported on a finite discrete interval [0, n]. We introduce a new finite difference operator ∇n, defined as a linear combination of left and right finite differences. We show that this operator ∇n plays a key role in a new Poincaré (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk polynomials acting as eigenfunctions of the relevant operator. We briefly discuss the relationship of this operator to the problem of optimal transport...
A natural localization of Hardy spaces in several complex variables
Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in . The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop’s property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.
A nearly uniformly convex space which is not a -space
A necessary and sufficient condition for existence of extremal functions of a linear functional on .
A negative result in differentiation theory
A Neumann problem with the -Laplacian on a solid torus in the critical of supercritical case.
A new algorithm for approximating the least concave majorant
The least concave majorant, , of a continuous function on a closed interval, , is defined by We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on . Given any function , it can be well-approximated on by a clamped cubic spline . We show that is then a good approximation to . We give two examples, one to illustrate, the other to apply our algorithm.