Advanced Search

0. Introduction. Nous donnons ici une étude systématique des systèmes doublement orthogonaux "de Bergman" et leurs applications à certains aspects de l'analyse pluricomplexe: espaces de fonctions holomorphes, fonctions séparément analytiques. C'est en quelque sorte un article de synthèse. On y trouve cependant des démonstrations détaillées qui n'ont paru nulle part ailleurs.

We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces $H^{p_k}$, $0<p_k\le 1$, to Lebesgue spaces $L^p$. These conditions are expressed in terms of L²-based Sobolev spaces with sharp indices within the classes of multipliers we consider. Our results extend those obtained in the linear case (m = 1) by Calderón and Torchinsky (1977) and in the bilinear case (m = 2) by Miyachi and Tomita (2013). We also prove a coordinate-type Hörmander integral condition...

The problem of testing hypothesis under which the observations are independent, identically distributed against a class of alternatives of regression in a parameter of the one-parameter exponential family is studied. A parametric test for this problem is suggested. The relative efficiency of the parametric test compared to the rank test proposed in the author's preceding paper is also derived.

CONTENTSIntroduction......................................................................................................................................... 5I. Prediction of strictly stationary random fields.................................................................................... 6II. Prediction of stationary-in-norm fields in Banach spaces of random variables........................ 23 § 1. Banach spaces of random variables...................................................................................

CONTENTSIntroduction............................................................................................................................................................................ 51. Notation and preliminaries............................................................................................................................................ 52. Statement of the problem..................................................................................................................................................

CONTENTSIntroduction..........................................................................................................................................................5Preliminaries........................................................................................................................................................7   1. Linear spaces and linear operators..............................................................................................................7   2. Right...

We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.

The regression model X(t),Y(t);t=1,...,n with random explanatory variable X is transformed by prescribing a partition $S_1,...,S_k$ of the given domain S of X-values and specifying$X\left(1\right),...,X\left(n\right)\cap S_i=X_{i1},...,X_{i\alpha \left(i\right)},i=1,...,k.$Through the conditioning$\alpha \left(i\right)=a\left(i\right),i=1,...,k,X_{i1},...,X_{i\alpha \left(i\right)};i=1,...,k=x_{11},...,x_{ka\left(k\right)}$the initial model with i.i.d. pairs (X(t),Y(t)),t=1,...,n, becomes a conditional fixed-design $(x_{11},...,x_{ka\left(k\right)})$ model$Y_{ij},i=1,...,k;j=1,...,a\left(i\right)$where the response variables $Y_{ij}$ are independent and distributed according to the mixed conditional distribution $Q(·,x_{ij})$ of Y given X at the observed value $x_{ij}$.Afterwards, we investigate the case$\left(Q\right)E\left(Y^{\text{'}}\right|x)={\sum }_{i=1}^k{b}_i\left(x\right){\theta }_i{I}_{S_i}\left(x\right),\left(Q\right)D\left(Y\right|x)={\sum }_{i=1}^k{d}_i\left(x\right){\Sigma }_i{I}_{S_i}\left(x\right)$which arises when...

We consider a system of linear response models with random explanatory variables in which the global matrix parameter is subject to arbitrary constraints. A generalized least squares estimate (GLSE) of the global parameter is defined by its property of minimizing some norm of the global residual over an affine manifold, called the support, containing the global parameter range. The crucial relation is the one between the true global parameter value and the so-called global mean square (msq) regression...