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Square functions for wavelet type systems

Gevorkjan G., Wolnik B.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

155-171

We show the equivalence of the L[sub p] (0 < p [a is less than or equal to] 2) (quasi)-norms of square functions for the systems {2 [...], where f satisfies some decay condition. This implies the boundedness of the shift operator on the wavelet type unconditional basis on L[sub p], 1 < p < [infinity]. We prove also that such operator is unbounded on L[sub 1].