The ... Problem with Uniform Bounds on Derivatives.
It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.
We give some explicit values of the constants and in the inequality where denotes the norm of the Bergman projection on the space.
Let be a tuple of commuting operators on a Banach space . We discuss various conditions equivalent to that the holomorphic (Taylor) functional calculus has an extension to the real-analytic functions or various ultradifferentiable classes. In particular, we discuss the possible existence of a functional calculus for smooth functions. We relate the existence of a possible extension to existence of a certain (ultra)current extension of the resolvent mapping over the (Taylor) spectrum of . If ...
We study the -equation with Hölder estimates in -convex wedges of by means of integral formulas. If is defined by some inequalities , where the real hypersurfaces are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the ’s have at least positive eigenvalues, we solve the equation for each continuous -closed form in , , with the following estimates: if denotes the distance to the boundary of and if is bounded, then for all ,...
We derive formulas for the values in the interior of the L2-minimal solutions of the ∂∂-equation in the unit ball of Cn. These formulas generalize previously known formulas for the boundary values of the same solutions. We estimate the solution and obtain a (known) result concerning weighted Nevanlinna classes.