A weighted norm inequality for Fourier series

Approximation by trigonometric polynomials in weighted Orlicz spaces

“…Taking the boundedness of the linear operators f → S n (·, f ) and f → f in L p (T, ω) into account [17,18] and using the method of proof of Lemma 1, one can show that…”

Approximation by trigonometric polynomials in weighted rearrangement invariant spaces

“…Since the linear operators f → S n (·, f ) and f → f are bounded in the weighted Lebesgue spaces L p (T, ω) [16,17], by using the method of proof of Lemma 2.2, one can show that…”

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

“…For this step we refer to [21] where the following goodlambda inequality is proved, for a decomposition of {Cf (x) > λ} into pairwise disjoint intervals (I j ) j :…”