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Fourier multipliers on weighted spaces
The paper provides a complement to the classical results on Fourier
multipliers on spaces. In particular, we prove that if and a
function is of bounded -variation
uniformly on the dyadic intervals in , i.e. , then is a Fourier multiplier on
for every and every weight satisfying Muckenhoupt's
-condition. We also obtain a higher dimensional counterpart of this
result as well as of a result by E. Berkson and T.A. Gillespie including the
case of the spaces with . New weighted estimates for
modified Littlewood-Paley functions are also provided.Comment: The statement of Theorem B(ii) for q in (1,2) is revised. The main
results of the paper (i.e., Theorems A, B(i), and C) are left unchange
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