In this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted Dirichlet spaces or Bloch type spaces to $Q_K$ type spaces.

Let Ω be an open bounded set in R n (n ≥ 2), with C 2 boundary, and N p,λ (Ω) (1 < p < +∞, 0 ≤ λ < n) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti inequality and we exploit it to show that, under a suitable condition of Cordes type, the Dirichlet problem:

we give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(c_{omega_1,varphi_1}^*‎ , ‎c_{omega_2,varphi_2}^*)$ on the hilbert space $mathcal{h}$ of analytic functions is supercyclic‎.

We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...

Let Γ be a closed Jordan curve, and f the conformal mapping that sends unit disc D onto interior domain of Γ. If logf′ belongs to Dirichlet space D, we call Weil-Petersson curve. The purpose this note is extend recent results, obtained by G. Cui Ch. Bishop in case curves, when either some Qp,0, space, for 0<p≤1, or weighted-Dirichlet contained D. More precisely, will characterize quasiconformal...

We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, polynomial mixing property is established. This done in the setting kinetic taking values an $$L^1$$ -weighted space.