We characterize continuity and compactness of the Volterra integral operator $T_g$ with non-constant analytic symbol $g$ between certain weighted Fréchet or (LB)-spaces functions on open unit disc, which arise as projective (resp. inductive) limits intersections unions) Bergman spaces order $1<p<\infty$ induced by standard radial weight $(1-|z|^2)^\alpha$ for $0<\alpha&...

The spectrum of the Ces?ro operator C is determined on spaces which arises as intersections Ap ?+ (resp. unions ?-) Bergman Ap? order 1 < p induced by standard radial weights (1-|z|)?, for 0 ? 1. We treat them reduced projective limits inductive limits) weighted Ap?, with respect to ?. Proving that these admit monomials a Schauder basis paves way using Grothendieck-Pietsch criterion deduce w...

Let $$\mu _\alpha$$ be the Lebesgue plane measure on unit disk with radial weight $$\frac{\alpha +1}{\pi }(1-|z|^2)^\alpha$$ . Denote by $${\mathcal {A}}^{2}_{n}$$ space of n-analytic functions $${\mathbb {D}}$$ , square-integrable respect to Extending results Ramazanov (1999, 2002), we explain that polynomials (studied Koornwinder in 1975 and Wünsche 2005) form an orthonormal basis Using this ...