algebras and the symbolic calculus of Sebastião e Silva. (Les algèbres et le calcul symbolique de Sebastião e Silva.)
We study the structure of spaces of germs of holomorphic functions on compact sets in Fréchet spaces for (LB∞) as well as for (Ω,Ω).
The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the case have a Denjoy-Carleman counterpart.
We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces , 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the spaces in terms of the coefficients of wavelet decompositions.
The -weighted Besov spaces of holomorphic functions on the unit ball in are introduced as follows. Given a function of regular variation and , a function holomorphic in is said to belong to the Besov space if where is the volume measure on and stands for the fractional derivative of . The holomorphic Besov space is described in the terms of the corresponding space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also,...