Extension of a Theorem of Fejér to Double Fourier-Stieltjes Series.
One of the main results in modern harmonic analysis is the extrapolation theorem of J. L. Rubio de Francia for Ap weights. In this paper we discuss some recent extensions of this result. We present a new approach that, among other things, allows us to obtain estimates in rearrangement-invariant Banach function spaces as well as weighted modular inequalities. We also extend this extrapolation technique to the context of A∞ weights. We apply the obtained results to the dyadic square function. Fractional...
We prove that if and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where is the space of multipliers of .