Displaying similar documents to “On an extrapolation theorem of Carleson-Sjölin type with applications to a.e. convergence of Fourier series”

On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity.

María Jesús Carro (2002)

Publicacions Matemàtiques


Given a sublinear operator T satisfying that ||Tf||Lp(ν) ≤ C/(p-1) ||f||Lp(μ), for every 1 < p ≤ p0, with C independent of f and p, it was proved in [C] that... [check the paper abstract for the formula] This estimate implies that T: L log L → B, where B is a rearrangement invariant space. The purpose of this note is to give several...

Remarks on a theorem by N. Yu. Antonov

Per Sjölin, Fernando Soria (2003)

Studia Mathematica


We extend some results of N. Yu. Antonov on convergence of Fourier series to more general settings. One special feature of our work is that we do not assume smoothness for the kernels in our hypotheses. This has interesting applications to convergence with respect to general orthonormal systems, like the Walsh-Fourier system, for which we prove a.e. convergence in the class L log L log log log L. Other applications are given in the theory of differentiation of integrals.

Absolute values of BMOA functions.

Konstantin M. Dyakonov (1999)

Revista Matemática Iberoamericana


The paper contains a complete characterization of the moduli of BMOA functions. These are described explicitly by a certain Muckenhoupt-type condition involving Poisson integrals. As a consequence, it is shown that an outer function with BMO modulus need not belong to BMOA. Some related results are obtained for the Bloch space.

Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds, Petr Gurka, Bohumír Opic (1995)

Studia Mathematica


This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.