In this paper, we obtain one-sided and two-sided Tauberian conditions of Landau Hardy types for (C,1,0) (C,0,1) summability methods improper double integrals under which convergence follows from integrals. We give similar results (C,1,1) method general, in terms the concepts slowly decreasing (resp. oscillating) strong functions different senses Ces?ro real or complex-valued locally integrable ...

We prove L p $L^{p}$ -boundedness of variational Carleson operators for functions valued in intermediate UMD spaces. This provides quantitative information on the rate convergence partial Fourier integrals vector-valued functions. Our proof relies bounds wave packet embeddings into outer Lebesgue spaces time-frequency-scale space R + 3 $\mathbb {R}^{3}_{+}$ , which are focus this paper.

After the pioneer work of Calderón and Zygmund in the 50’s, the systematic study of singular integrals has become a corner stone in harmonic analysis with deep implications in mathematical physics, partial differential equations and other mathematical disciplines. Subsequent generalizations of Calderón-Zygmund theory have essentially pursued two lines. We may either consider more general domain...

Abstract We establish the local Lipschitz continuity and higher differentiability of vector-valued minimizers a class energy integrals Calculus Variations. The main novelty is that we deal with possibly degenerate densities respect to