Some topics concerning integrals of derivatives and difference quotients on metric spaces

Some topics concerning harmonic analysis on metric spaces

In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.

Some topics concerning analysis on metric spaces and semigroups of operators

This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.

关于Brezis等人提出的关于一阶Sobolev空间临界差商刻画的两个问题

On Two Questions by Brezis et al Concerning the Critical Difference Quotient Characterization of First-Order Sobolev Spaces

本文针对Brezis等人提出的两个问题，证明在例外参数范围内齐次Hardy--Sobolev空间严格嵌入BV和W^{1,1}变体空间，且这些空间的商空间不可赋范。

Some questions related to fractals

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

Some remarks concerning integrals of curvature on curves and surfaces

In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using quarternions or Clifford algebras. These topics came up in "Analysis of and on Uniformly Rectifiable Sets" (with Guy David, American Mathematical Society, 1993), and here we describe some of the basic points involved. A presentation based on this paper was made at the AMS Special Session "Surface Geometry and Shape Perception" (Hoboken, 2001).

Oscillatory and Fourier Integral operators with degenerate canonical relations

We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.