This paper presents selected results on the study of the onedimensional property of holomorphic continuations of functions defined on the boundary of a bounded domain in Cn. This paper presents selected results on holomorphic continuation of functions defined on the boundary of a bounded domain D ⊂ C, n > 1, into this domain. We consider functions with a one-dimensional holomorphic continuation...

We give a generalization of the Penrose transform on Hermitian manifolds with metrics locally conformally equivalent to Bochner-Kähler metrics. We also give an explicit formula for the inverse transform. 1991 Mathematics Subject Classification: 32L25 (Primary), 53C55, 32C35 (Secondary)

A classical theorem of Bochner asserts that the isometry group a compact Riemannian manifold with negative Ricci curvature is finite. In this paper we give several extensions Bochner’s by allowing “small” positive curvature.

We study the construction of extrapolation spaces operator-valued multiplication operators on Bochner Lp-spaces by means Lp-fiber spaces.

Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 − |ξ| − |η|)+ and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L × L into L with minimal smoothness, i.e., any δ > 0, and we obtain estimates for other pairs of spaces for...

where (h) is the inverse of the matrix (hij), ∆M = ∑ i,j h ∂ij and Γ s tγ denote the Christoffel symbols of the Hermitian metric g on N . It follows from (1.1) that if u is holomorphic, then u must be harmonic. Thus, it is natural to ask under what circumstances a harmonic map is holomorphic or antiholomorphic. Under the assumption that both M and N are compact, Siu [31] demonstrated that if th...

Well-posed space-time variational formulations in fractional order Bochner-Sobolev spaces are proposed for parabolic partial differential equations, and in particular for the instationary Stokes and Navier-Stokes equations on bounded Lipschitz domains. The latter formulations include the pressure variable as a primal unknown, and so account for the incompressibility constraint via a Lagrange mu...

We now consider the family of operators Tλ, λ ≥ 0, defined on Rn by T̂λ f (ξ) = mλ f̂ (ξ), where mλ(ξ) = (1− |ξ|)+. These are the Bochner-Riesz multipliers, which can be viewed as an attempt to smooth out the singularity of the disc multiplier to see if we can obtain boundedness on a wider range of Lp spaces. Note that when λ = 0 we obtain S1, and that as λ increases, the multiplier mλ becomes sm...