In this paper, the Lvp(R)-boundedness of the Dunkl–Hausdorff operator Hα,φ f (x) = ZR ||tφ(|2αt+)|2 f ( xt ) dt has been characterized and for a certain type of weight v, the operator norm kHα,φkLvp(R)→Lvp(R) has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.
BOUNDEDNESS of the DUNKL–HAUSDORFF OPERATOR in LEBESGUE SPACES / Jain, S.; Fiorenza, A.; Jain, P.. - In: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. - ISSN 0035-7596. - 51:6(2021), pp. 2031-2044. [10.1216/rmj.2021.51.2031]
BOUNDEDNESS of the DUNKL–HAUSDORFF OPERATOR in LEBESGUE SPACES
Fiorenza A.;
2021
Abstract
In this paper, the Lvp(R)-boundedness of the Dunkl–Hausdorff operator Hα,φ f (x) = ZR ||tφ(|2αt+)|2 f ( xt ) dt has been characterized and for a certain type of weight v, the operator norm kHα,φkLvp(R)→Lvp(R) has been obtained. This covers several of the existing results. Analogous results in two dimensions have also been proved.File in questo prodotto:
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