Abstract We characterize all pairs of entire functions $$(u,\psi )$$ ( u , ψ ) for which the induced weighted superposition operator $$S_{(u,\psi )}$$ S transforms one Fock space ...

We obtain sharp L p → q $L^p\rightarrow L^q$ hypercontractive inequalities for the weighted Bergman spaces on unit disk D $\mathbb {D}$ with usual weights α − 1 π ( | z 2 ) , > $\frac{\alpha -1}{\pi }{(1-|z|^2)}^{\alpha -2},\alpha >1$ ⩾ $q\geqslant 2$ thus solving an interesting case of a problem from Janson [Ark. Math. 21 (1983), no. 1, 97–110]. also give some estimates 0 < $0<q<2$ .

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact $L^{p_1}(w_1)$ $w_1\in R^d)$. Then $L^p(w)$ $p\in(1,\infty)$ $w\in A_p(\mathbb This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from combination results the interpolation theory spaces one h...