Summability of Multi-Dimensional Fourier Series and Hardy Spaces

262 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

The Segal Algebra ${\bf S}_0({\Bbb R}^d)$ and Norm Summability of Fourier Series and Fourier Transforms (2006, background): “It is easy to see that the spaces LpðX d Þð 14 p 35 ]) are homogeneous Banach spaces.”
New martingale inequalities and applications to Fourier analysis (2018, methodology): “7 gives back the well known result of Weisz ([74, 78]) mentioned above when φ(x, t) := t for any x ∈ [0, 1) and t ∈ (0,∞), with p ∈ ((1) 2 ,∞).”
The Hardy-Lorentz Spaces $H^{p,q}(R^n)$ (2007, methodology): “This approach combines the concept of p-quasi local operator of Weisz, see [17], with the idea of variable dilations of R.”
Wiener amalgams and pointwise summability of Fourier transforms and Fourier series (2006, background): “It is easy to see that Marcinkiewicz and Zygmund density theorem holds also if we have the inequality (4·12) instead of a weak type (1, 1) inequality (see the proof in Weisz [43]).”