A Stone-Weierstrass theorem for Banach lattices
A strong convergence in and upper -continuous operators
A strongly extreme point need not be a denting point in Orlicz spaces equipped with the Orlicz norm
There are necessary conditions for a point x from the unit sphere to be a denting point of the unit ball of Orlicz spaces equipped with the Orlicz norm generated by arbitrary Orlicz functions. In contrast to results in [12, 17, 16], we present also examples of Orlicz spaces in which strongly extreme points of the unit ball are not denting points.
A subelliptic Bourgain–Brezis inequality
We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space by functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for on the Heisenberg group .
A summability condition on the gradient ensuring BMO.
A system of exponential functions with shift and the Kostyuchenko problem.
A THeorem of Global Existence of Solutions to Nonlinear Wave Equations in Four Space Dimensions.
A theorem on kernel in the theory of operator-valued distributions
A theorem on operator algebras.
A theorem on the weak topology of C(X) for compact scattered X
A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces.
A topology on inequalities.
A trace inequality for generalized potentials
A transplantation theorem for ultraspherical polynomials at critical index
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with .
A two weight weak inequality for potential type operators
We give conditions on pairs of weights which are necessary and sufficient for the operator to be a weak type mapping of one weighted Lorentz space in another one. The kernel is an anisotropic radial decreasing function.
A unified approach for commutators theorems in interpolation theory, a survey.
We review the main facts that are behind a unified construction for the commutator theorem of the main interpolation methods.
A uniqueness theorem for higher order elliptic partial differential equations.
A universal Lipschitz extension property of Gromov hyperbolic spaces.
A version of the Grothendieck theorem for subspaces of analytic functions in lattices.
A Vey theorem for nonlinear PDE