Singular integrals, maximal functions and Fourier restriction to spheres: the disk multiplier revisited (Q908061)

The author revisits a series of results related to the Bochner-Riesz operator conjecture. The consideration includes the classical Calderón-Zygmund singular integral operators, directional Hilbert transforms, Kakeya maximal functions, disc multipliers, and some other important objects in Fourier analysis. The main concern is the boundedness of the operators under consideration in the space \(L^p_{\mathrm{rad}} L^2_{\mathrm{ang}}(R^n)\). Some known arguments and estimates are improved.