On Weyl multipliers of non-overlapping Franklin polynomial systems

Abstract

We prove that $\log n$ is an almost everywhere convergence Weyl multiplier for any orthonormal system of non-overlapping Franklin polynomials. It will also be remarked that $\log n$ is the optimal sequence in this context.

more general results for wavelet type systems were obtained in arXiv:2104.03124

References in corpus (1)

• Singular Integrals Along N Directions in R^2