Conjugacy for Fourier–Bessel expansions
Volume 176 / 2006
Studia Mathematica 176 (2006), 215-247
MSC: Primary 42C10; Secondary 44A20.
DOI: 10.4064/sm176-3-3
Abstract
We define and investigate the conjugate operator for Fourier–Bessel expansions. Weighted norm and weak type $(1,1)$ inequalities are proved for this operator by using a local version of the Calderón–Zygmund theory, with weights in most cases more general than $A_p$ weights. Also results on Poisson and conjugate Poisson integrals are furnished for the expansions considered. Finally, an alternative conjugate operator is discussed.
