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Some criteria for determining when a Walsh series is a Walsh-Fourier series
Abstract
We show that a general Walsh series is the
Walsh-Fourier series of a function ∈ 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 ∈ LΦ[0,1],
the Orlicz space generated by an N-function Φ.
Mathematics Subject Classification (2000): 42C10, 46E30
Key words: Walsh series, Orlicz spaces
Quaestiones Mathematicae 26(2003), 267278
Walsh-Fourier series of a function ∈ 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 ∈ LΦ[0,1],
the Orlicz space generated by an N-function Φ.
Mathematics Subject Classification (2000): 42C10, 46E30
Key words: Walsh series, Orlicz spaces
Quaestiones Mathematicae 26(2003), 267278
