Note on Fourier analysis. XXXI. Cesàro summability of Fourier series
نویسندگان
چکیده
منابع مشابه
On the Summability of Fourier Series. Fifth Note.
and evaluating the generalized sum of (1) as the lim rm(x; f). The matrix ?2 will be subjected to the restrictions (i-iv) below. These restrictions are of such general nature, however, that they are satisfied by a great majority of the definitions of summability known in the literature. Our first condition on 21 is significant only in the case where 91 is of infinite reference. It is automatica...
متن کاملLogarithmic Summability of Fourier Series
A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.
متن کاملOn the convergence and Cesàro summability of trigonometric Fourier series of monotone type functions
The behaviour of Cesàro means of trigonometric Fourier series of monotone type functions in the space of continuous functions is studied.
متن کاملl1-summability of higher-dimensional Fourier series
It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...
متن کاملSummability of Multi-Dimensional Trigonometric Fourier Series
We consider the summability of oneand multi-dimensional trigonometric Fourier series. The Fejér and Riesz summability methods are investigated in detail. Different types of summation and convergence are considered. We will prove that the maximal operator of the summability means is bounded from the Hardy space Hp to Lp, for all p > p0, where p0 depends on the summability method and the dimensio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1952
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1952.2.419