We give some rather weak sufficient condition for boundedness of the Marcinkiewicz integral operator on the product spaces (1 < p < ∞), which improves and extends some known results.
We prove two-weight norm inequalities in ℝⁿ for the minimal operator , extending to higher dimensions results obtained by Cruz-Uribe, Neugebauer and Olesen [8] on the real line. As an application we extend to ℝⁿ weighted norm inequalities for the geometric maximal operator , proved by Yin and Muckenhoupt [27]. We also give norm inequalities for the centered minimal operator, study powers of doubling weights and give sufficient conditions for the geometric maximal operator to be equal to the closely...
We introduce the minimal operator on weighted grand Lebesgue spaces, discuss some weighted norm inequalities and characterize the conditions under which the inequalities hold. We also prove that the John-Nirenberg inequalities in the framework of weighted grand Lebesgue spaces are valid provided that the weight function belongs to the Muckenhoupt class.
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.
For we calculate the norm of the Fourier transform from the space on a finite abelian group to the space on the dual group.
We introduce the one-sided minimal operator, , which is analogous to the one-sided maximal operator. We determine the weight classes which govern its two-weight, strong and weak-type norm inequalities, and show that these two classes are the same. Then in the one-weight case we use this class to introduce a new one-sided reverse Hölder inequality which has several applications to one-sided weights.
We give the first term of the asymptotic development for the phase of the N-th (minimum-phased) Daubechies filter as N goes to +∞. We obtain this result through the description of the complex zeros of the associated polynomial of degree 2N+1.
The author studies a system of polynomials orthogonal at a finite set of points its weight approximating that of the orthogonal system of classical Jacobi polynomials.