Riesz means of Fourier transforms and Fourier series on Hardy spaces

• Autorzy: Ferenc Weisz
• Języki publikacji: EN

Abstrakty

EN

Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_p(ℝ)$ to $L_p(ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_p(ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ ∈ L_1(ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_p(ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ ∈ H_p(ℝ)$, the Riesz means converge to ⨍ in $H_p(ℝ)$ norm (1/(α+1) < p < ∞). The same results are proved for the conjugate Riesz means and for Fourier series of distributions.

Słowa kluczowe

EN

Hardy spaces; p-atom; atomic decomposition; interpolation; Fourier transforms; Riesz means

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 42A24: Summability and absolute summability of Fourier and trigonometric series
• 42B08: Summability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 131
• Numer: 3
• Strony: 253-270

Daty

wydano

1998-02-05

otrzymano

1997-09-17

Twórcy

autor

Ferenc Weisz

• Department of Numerical Analysis, Eötvös L. University, Múzeum krt. 6-8, H-1088 Budapest, Hungary

Bibliografia

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