Some criteria for determining when a Walsh Series is a Walsh-Fourier Series
نویسندگان
چکیده
We show that a general Walsh series is the Walsh-Fourier series of a function f ∈ Lp[0, 1] for 1 ≤ p <∞ if and only if its sequence of partial sums contains a relatively weakly compact subsequence. Several other criteria are established for the case where f ∈ LΦ[0, 1], the Orlicz space generated by an N -function Φ. Mathematics subject classification (2000): 42C10, 46E30
منابع مشابه
On the Uniform Convergence and L-convergence of Double Fourier Series with Respect to the Walsh–kaczmarz System
In this paper we study the approximation by rectangular partial sums of a double Fourier series with respect to the Walsh–Kaczmarz system in the spaces C and L. From our results we obtain different criteria of the uniform convergence and L-convergence of a double Fourier–Kaczmarz series. 2000 Mathematics Subject Classification: Primary 41A50; Secondary 42C10.
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