In this paper, we investigate the role of square functions defined for a d-tuple commuting Ritt operators $$(T_1,\ldots ,T_d)$$ acting on general Banach space X. Firstly, prove that if admits $$H^\infty $$ joint functional calculus, then it verifies various function estimates. Then study converse when every $$T_k$$ is R-Ritt operator. Under last hypothesis, and X K-convex space, show estimates ...

In this paper, we first introduce a class of nonlinear mappings called generic generalized nonspreading which contains the class of generalized nonspreading mappings in a Banach space and then prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear m...

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new class of methods for nonparametric regression. Given a data set of input-response pairs, the DP-GLM produces a global model of the joint distribution through a mixture of local generalized linear models. DP-GLMs allow both continuous and categorical inputs, and can model the same class of responses that can be mo...

We prove that translation invariant multilinear operators of restricted weak type (1, 1, . . . , 1, q) must necessarily be of weak type (1, 1, . . . , 1, q). We give applications.

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.

We give a complete solution to the Borel–Ritt problem in non-uniform spaces $${\mathscr {A}}^-_{(M)}(S)$$ of ultraholomorphic functions Beurling type, where S is an unbounded sector Riemann surface logarithm and M strongly regular weight sequence. Namely, we characterize surjectivity existence continuous linear right inverse asymptotic Borel map on terms aperture sequence M. Our work improves p...

A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...