4.2 Article

An Analogy of the Carleson-Hunt Theorem with Respect to Vilenkin Systems

Related references

Note: Only part of the references are listed.
Article Mathematics

Convergence of Vilenkin-Fourier series in variable Hardy spaces

Ferenc Weisz

Summary: This article investigates variable Hardy and HardyLorentz spaces satisfying the log-Holder condition and containing Vilenkin martingales. It proves the convergence of the partial sums of the Vilenkin-Fourier series in L-p((.))- and L-p(.),L-q-norm, as well as the boundedness of the maximal operator of the Fejer means in H(p(.)) to L-p(.) and H-p(.),H-q to L-p(i)q. The condition for boundedness in the last result is surprising and not required for Fourier series or Fourier transforms.

MATHEMATISCHE NACHRICHTEN (2022)

Article Mathematics

On Sjolin-Soria-Antonov type extrapolation for locally compact groups and a.e. convergence of Vilenkin-Fourier series

G. Oniani

Summary: The theorem proves an extrapolation result for certain types of groups, showing convergence of Fourier series for specific classes of functions in the specified group setting.

ACTA MATHEMATICA HUNGARICA (2021)

Article Mathematics

The Polynomial Carleson operator

Victor Lie

ANNALS OF MATHEMATICS (2020)

Article Mathematics, Applied

NORM CONVERGENCE OF LOGARITHMIC MEANS ON UNBOUNDED VILENKIN GROUPS

Gyorgy Gat et al.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS (2018)

Article Mathematics

A GUIDE TO CARLESON'S THEOREM

Ciprian Demeter

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS (2015)

Article Mathematics

Logarithmic L p Bounds for Maximal Directional Singular Integrals in the Plane

Ciprian Demeter et al.

JOURNAL OF GEOMETRIC ANALYSIS (2014)

Article Mathematics, Applied

Lp ESTIMATES FOR THE HILBERT TRANSFORMS ALONG A ONE-VARIABLE VECTOR FIELD

Michael Bateman et al.

ANALYSIS & PDE (2013)

Article Mathematics, Applied

SINGULAR INTEGRALS ALONG N DIRECTIONS IN R2

Ciprian Demeter

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2010)

Article Mathematics

Breaking the duality in the return times theorem

Ciprian Demeter et al.

DUKE MATHEMATICAL JOURNAL (2008)

Article Mathematics, Applied

Almost everywhere convergence of fejer means of L1 functions on rarely unbounded vilenkin groups

Gyoergy Gat

ACTA MATHEMATICA SINICA-ENGLISH SERIES (2007)

Article Mathematics

Cesaro means of integrable functions with respect to unbounded Vilenkin systems

G Gát

JOURNAL OF APPROXIMATION THEORY (2003)

Article Mathematics, Applied

A Carleson type theorem for a Cantor group model of the scattering transform

C Muscalu et al.

NONLINEARITY (2003)