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
A weak invertibility criterion in the weighted -spaces of holomorphic functions in the ball.
A weak molecule condition for certain Triebel-Lizorkin spaces
A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.
A Whitney extension theorem in and Besov spaces
The classical Whitney extension theorem states that every function in Lip, , closed, , a non-negative integer, can be extended to a function in Lip. Her Lip stands for the class of functions which on have continuous partial derivatives up to order satisfying certain Lipschitz conditions in the supremum norm. We formulate and prove a similar theorem in the -norm.The restrictions to , , of the Bessel potential spaces in and the Besov or generalized Lipschitz spaces in have been...
A Тote on the Сompleteness of
A₁-regularity and boundedness of Calderón-Zygmund operators
The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...