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Conjugacy for Fourier-Bessel expansions

Óscar CiaurriKrzysztof Stempak — 2006

Studia Mathematica

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.

Solving dual integral equations on Lebesgue spaces

Óscar CiaurriJosé GuadalupeMario PérezJuan Varona — 2000

Studia Mathematica

We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh’s type. We reformulate these equations giving a better description in terms of continuous operators on L p spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series n = 0 c n J μ + 2 n + 1 which converges in the L p -norm and almost everywhere, where J ν denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution....

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