Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

• Autorzy: Ferenc Weisz
• Języki publikacji: EN

Abstrakty

EN

The martingale Hardy space $H_p([0,1)^2)$ and the classical Hardy space $H_p(𝕋^2)$ are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from $H_p$ to $L_p$ (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a Marcinkiewicz-Zygmund type inequality is obtained for BMO spaces.

Słowa kluczowe

EN

martingale and classical Hardy spaces; p-atom; atomic decomposition; Walsh functions; Hardy-Littlewood inequality

Kategorie tematyczne

• 42B05: Fourier series and coefficients
• 60G42: Martingales with discrete parameter
• 43A75: Analysis on specific compact groups
• 42B08: Summability
• 42B30: H p -spaces
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995-1996
• Tom: 117
• Numer: 2
• Strony: 173-194

Daty

wydano

1996

otrzymano

1995-05-05

Twórcy

autor

Ferenc Weisz

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

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