By applying Pitt’s inequality we prove a weighted L^p version of Gallagher’s inequality for trigonometric series. Furthermore, we consider a family of weights generated by a smoothing process, via convolution operation, whose first steps are the indicator function of a compact interval and the so-called Cesàro weight supported in the same interval. The eventual aim is the comparison of such weights in view of possible refinements of our inequality for p=2.
A weighted inequality for trigonometric series / Laporta, Maurizio; Coppola, Giovanni. - In: THE JOURNAL OF ANALYSIS. - ISSN 2367-2501. - 31:2(2023), pp. 1041-1056. [10.1007/s41478-022-00486-y]
A weighted inequality for trigonometric series
Maurizio Laporta
;Giovanni Coppola
2023
Abstract
By applying Pitt’s inequality we prove a weighted L^p version of Gallagher’s inequality for trigonometric series. Furthermore, we consider a family of weights generated by a smoothing process, via convolution operation, whose first steps are the indicator function of a compact interval and the so-called Cesàro weight supported in the same interval. The eventual aim is the comparison of such weights in view of possible refinements of our inequality for p=2.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
