Riesz means associated with certain product type convex domain

Hong, Sungeon; Kim, Joonil; Yang, Chan Woo

doi:10.1016/j.jmaa.2011.02.070

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Cited by 9 publications

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“…The following result generalizes one by Stein, Taibleson and Weiss [39] for the standard Bochner-Riesz means. Other generalizations for specific rough ρ were considered in [19] and the references therein.…”

Section: Maximal Functions On Hmentioning

confidence: 99%

Riesz means of Fourier series and integrals: Strong summability at the critical index

Kim

Seeger

2019

Trans. Amer. Math. Soc.

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We consider spherical Riesz means of multiple Fourier series and some generalizations. While almost everywhere convergence of Riesz means at the critical index (d − 1)/2 may fail for functions in the Hardy space h 1 (T d ), we prove sharp positive results for strong summability almost everywhere. For functions in L p (T d ), 1 < p < 2, we consider Riesz means at the critical index d(1/p − 1/2) − 1/2 and prove an almost sharp theorem on strong summability. The results follow via transference from corresponding results for Fourier integrals. We include an endpoint bound on maximal operators associated with generalized Riesz means on Hardy spaces H p (R d ) for 0 < p < 1.

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Section: Maximal Functions On Hmentioning

confidence: 99%

Riesz means of Fourier series and integrals: Strong summability at the critical index

Kim

Seeger

2019

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…We can also obtain an L 4 R 3 estimate by combining square function arguments for the Nikodym maximal function with light rays (see [5]). Owing to the complex interpolation between the results on L 4 R 3 for δ > 0 and on L ∞ R 3 for δ > 1 2 , we obtain the desired bound for δ > max {2| 1…”

Section: Introductionmentioning

confidence: 99%