La fundamentación del análisis de Fourier

El análisis de Fourier tiene que ver con cuestiones como las de representar funciones periódicas de variable real..

Conjugate Hardy's inequalities with decreasing weights

We prove that for a decreasing weight ω on R+, the conjugate Hardy transform is bounded on Lp(ω ) (1 ≤ p < ∞ ) if and only if it is bounded on the cone of all decreasing functions of Lp(ω ). This property does not depend on p

Un teorema de coincidencia

Si cp(t) = kt (0 5 k c 1), el teorema de la aplicación con tractiva asegura la existencia y unicidad de solución par

Interpolation of families

We identify the intermédiate space of a complex interpolation family - in the sense of Coifman, Cwikel, Rochberg, Sagher and Weissof LP spaces with change of measure, for the complex interpolation method associated to an analytic functional

Entropy function spaces and interpolation

We associate to every function space, and to every entropy function E, a scale of spaces Λp,q (E) similar to the classical Lorentz spaces Lp,q. Necessary and sufficient conditions for they to be normed spaces are proved, their role in real interpolation theory is analyzed, and a number of applications to functional and interpolation properties of several variants of Lorentz spaces and entropy spaces are given

Conductor Sobolev-type estimates and isocapacitary inequalities

In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions