Generalized Stieltjes operators S_beta,mu are bounded on T_p^(alpha)(t^alpha) for 0 < beta - 1/p < mu, commute and factorize with generalized Cesaro operators, have explicitly represented spectra, with analogous results on the real line linking to Hilbert and Fourier transforms.
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Generalized Stieltjes and other integral operators on Sobolev-Lebesgue spaces
Generalized Stieltjes operators S_beta,mu are bounded on T_p^(alpha)(t^alpha) for 0 < beta - 1/p < mu, commute and factorize with generalized Cesaro operators, have explicitly represented spectra, with analogous results on the real line linking to Hilbert and Fourier transforms.