The ℓs\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz--Morrey spaces of the third kind

In the present paper, we will characterize the boundedness of the generalized fractional integral operators $I_{\rho}$ and the generalized fractional maximal operators $M_{\rho}$ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators $M_{\rho}$ and $I_{\rho}$ on generalized Orlicz--Morrey spaces

Rigidity and flexibility of surface groups

The aim of this work is the °exibility of the hyperbolic surfaces. The results are about °exibility and geometrical boundedness. Bers are stated the universal property for all hyperbolic surface of ¯nite area where introduced the constant of boundedness. We determine this constant, using symbolic dynamics