Recently the authors characterized Fredholmn properties of Toeplitz operators on weighted Fock spaces when Laplacian weight function is bounded below and above. In present work extend their characterization to doubling with a subharmonic whose measure. The geometry induced by Bergman metric for much more complicated than that Euclidean used in all previous cases study Fredholmness, which leads ...

One of the most fundamental problems in mathematics is to solve linear equations of the form Tf = g, where T is a linear transformation, g is known, and f is some unknown quantity. The simplest example of this comes from elementary linear algebra, which deals with solutions to matrix-vector equations of the form Ax = b. More generally, if V,W are vector spaces (or, in particular, Hilbert or Ban...

Let X be a locally convex topological vector space, Y a real Banach space, ƒ a mapping (in general, nonlinear) of X into Y. In several recent papers ([5], [ó], [7]), Pohozaev has studied the concept of normal solvability or the Fredholm alternative for mappings ƒ of class C. If Ax=f'x' is the continuous linear mapping of X into Y which is the derivative of ƒ a t the point x of X, A* the adjoint...

This paper studies the Fredholm properties for a class of regular hypoelliptic operators. We establish necessary and sufficient conditions priori estimates differential operators acting in multianisotropic Sobolev spaces R n . criteria index invariance are obtained wide on special scales weighted spaces.