ﻻ يوجد ملخص باللغة العربية
In this paper, we prove a $Tb$ theorem on product spaces $Bbb R^ntimes Bbb R^m$, where $b(x_1,x_2)=b_1(x_1)b_2(x_2)$, $b_1$ and $b_2$ are para-accretive functions on $Bbb R^n$ and $Bbb R^m$, respectively.
In this paper, we provide a non-homogeneous $T(1)$ theorem on product spaces $(X_1 times X_2, rho_1 times rho_2, mu_1 times mu_2)$ equipped with a quasimetric $rho_1 times rho_2$ and a Borel measure $mu_1 times mu_2$, which, need not be doubling but
Let $A$ be a compact set in $mathbb{R}$, and $E=A^dsubset mathbb{R}^d$. We know from the Mattila-Sjolins theorem if $dim_H(A)>frac{d+1}{2d}$, then the distance set $Delta(E)$ has non-empty interior. In this paper, we show that the threshold $frac{d+1}{2d}$ can be improved whenever $dge 5$.
By a result of Schur [J. Reine Angew. Math. 1911], the entrywise product $M circ N$ of two positive semidefinite matrices $M,N$ is again positive. Vybiral [Adv. Math. 2020] improved on this by showing the uniform lower bound $M circ overline{M} geq E
In this article, we extend a result of L. Loomis and W. Rudin, regarding boundary behavior of positive harmonic functions on the upper half space $R_+^{n+1}$. We show that similar results remain valid for more general approximate identities. We apply
In this paper we give a geometric condition which ensures that $(q,p)$-Poincare-Sobolev inequalities are implied from generalized $(1,1)$-Poincare inequalities related to $L^1$ norms in the context of product spaces. The concept of eccentricity plays