A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Let h be a measurable function defined on R+×R+. LetΩ∈ L(log L+)νq(Sn1-1×Sn2-1)(1 ≤νq≤ 2) be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral T f(x1, x2) = p. v.∫ Rn1+n2Ω(y′1, y′2)h(|y1|, |y2|)|y1|n1|y2|n2f(x1- y1, x2- y2)dy1dy2maps from Sα1, α2p, q˙F(Rn1× Rn2) boundedly to itself for 1 p, q ∞, α1, α2 ∈ R.     

Prime graphs of finite groups with a small number of triangles

The prime graph \(\Delta (G)\) of a finite group \(G\) is a graph whose vertices are the primes which divide the degrees of some irreducible complex characters of \(G\) and two distinct primes \(p\) and \(q\) are joined by an edge if the product \(pq\) divides some character degree of \(G\) . In this paper, we determine the upper bounds for the numbers of vertices of the prime graphs of finite groups which possess a small number of triangles. In some cases, we study the structure of such finite groups and their prime graphs in detail.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where

Blow‐up behavior of the Solution for the problem in a subdiffusive mediums

The diffusion problem in a subdiffusive medium is formulated by using the fractional differential operator. In this paper, we consider a fractional differential equation with concentrated source. The existence of the solution in a finite time is given. The finite time blow‐up criteria for the solution of the problem is established, and the location of the blow‐up point is investigated.     

Tangential extremal principles for finite and infinite systems of sets II: applications to semi-infinite and multiobjective optimization

This paper contains selected applications of the new tangential extremal principles and related results developed in Mordukhovich and Phan (Math Program 2011) to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.     

The Boundedness of Calderón-Zygmund Operators by Wavelet Characterization

This article deals with the boundedness properties of Calderón-Zygmund operators on Hardy spaces Hp(Rn). We use wavelet characterization of Hp(Rn) to show that a Calderón-Zygmund operator T with T*1 = 0 is bounded on Hp(Rn), n/n+ε p ≤ 1, where ε is the regular exponent of kernel of T . This approach can be applied to the boundedness of operators on certain Hardy spaces without atomic decomposition or molecular characterization.     

Bounds of <Emphasis Type="Italic">p</Emphasis>-adic weighted Hardy-Cesàro operators and their commutators on <Emphasis Type="Italic">p</Emphasis>-adic weighted spaces of Morrey types

In this paper we aim to investigate the boundedness of the p-adic weighted Hardy-Cesàro operators and their commutators on weighted functional spaces of Morrey type. In each case, we obtain the corresponding operator norms.