Almost everywhere convergence of Cesàro means of two variable Walsh – Fourier series with varying parameteres

A. A. Abu Joudeh; G. Gát

doi:10.37863/umzh.v73i3.196

A. A. Abu Joudeh Inst. Math., Univ. Debrecen, Hungary
G. Gát Inst. Math., Univ. Debrecen, Hungary

DOI: https://doi.org/10.37863/umzh.v73i3.196

Ключові слова: Cesàro means with varying parameters, two-dimensional Walsh-Fourier series, Marcinkiewicz means

Анотація

УДК 517.5

Збiжнiсть майже скрізь середнiх Чезаро для рядiв Уолша–Фур’є вiд двох змiнних зi змiнними параметрами

Доведено, що максимальний оператор вiд деяких середнiх $(C, \beta n)$ кубiчних часткових сум рядiв Уолша – Фур’є двох змiнних для iнтегровних функцiй має слабкий тип $(L_1,L_1)$. Бiльш того, $ (C , \beta_{n})$-середнi $\sigma_{2^n}^{\beta_{n}} f$ для функцiї $ f \in L_{1} $ збiгаються мaйже скрiзь до $f$ для $ f \in L_{1}(I^2) $, де $I$ — група Уолша для деяких послiдовностей $1> \beta_n \searrow 0$.

Посилання

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