Weighted transplantation for Fourier-Bessel series

We prove weighted transplantation inequalities for Fourier-Bessel series with weights more general than previously considered power weights. These inequalities follow by using a local version of the Calderón-Zygmund operator theory. The approach also allows us to obtain weighted weak type (1, 1) inequalities. As a typical application of transplantation inequalities, a multiplier result for the expansions considered is proved within a weighted setting with general weights. Research of the first author supported by Grant BFM2003-06335-603-03 of the DGI Research of the second author supported by KBN Grant #2 P03A 028 25.