Bergman Spaces For The Solutions Of Linear Partial Differential Equations.
Bessel generalized translations and some problems of approximation theory for functions on the half-line.
Bessel Transforms and Rational Extrapolation.
Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version
Mathematics Subject Classification: 26D10.The sharp constant is obtained for the Hardy-Stein-Weiss inequality for fractional Riesz potential operator in the space L^p(R^n, ρ) with the power weight ρ = |x|^β. As a corollary, the sharp constant is found for a similar weighted inequality for fractional powers of the Beltrami-Laplace operator on the unit sphere.
Best constants for some operators associated with the Fourier and Hilbert transforms
We determine the norm in , 1 < p < ∞, of the operator , where and are respectively the cosine and sine Fourier transforms on the positive real axis, and I is the identity operator. This solves a problem posed in 1984 by M. S. Birman [Bir] which originated in scattering theory for unbounded obstacles in the plane. We also obtain the -norms of the operators aI + bH, where H is the Hilbert transform (conjugate function operator) on the circle or real line, for arbitrary real a,b. Best...