Analytic dependence of orthogonal polynomials.
Remarks on the Hilbert transform and on some families of multiplier operators related to it.
We give an overview of the behavior of the classical Hilbert Transform H seen as an operator on L(R) and on weak-L(R), then we consider other operators related to H. In particular, we discuss various versions of Discrete Hilbert Transform and Fourier multipliers periodized in frequency, giving some partial results and stating some conjectures about their sharp bounds L(R) → L(R), for 1 < p < ∞.
Inequalities for Poisson integrals with slowly growing dimensional constants.
Sharp Lp estimates for the segment multiplier.
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