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On summability of the Fourier coefficients for functions from some Lorentz type spacesстатья
- Авторы: Nursultanov E.D., Kopezhanova A.N., L-E Persson
- Журнал: Preprint of Lulea University of Technology
- Том: 8
- Год издания: 2009
- Первая страница: 1
- Последняя страница: 27
- Аннотация: Let $\Lambda_\beta,$ $\beta>0,$ denote the Lorentz space equipped with the (quasi) norm $$ \|f\|_{\Lambda_\beta}:=\left(\int_0^1\left(f^*(t)t\lambda\left(\frac1t\right)\right)^\beta\frac{dt}{t}\right)^{\frac1\beta} $$ for a function $f$ on [0,1] and with $\lambda$ positive and equipped with some additional growth properties. Some estimates of this quantity and some corresponding sums of Fourier coefficients are proved for the case with a general orthonormal bounded system. Under certain circumstances even two sided estimates are obtained.
- Добавил в систему: Нурсултанов Ерлан Даутбекович