Some geometric aspects of Sobolev spaces
Global geometric aspects of Riemann-Hilbert problems.
Remarks on the Bourgain-Brezis-Mironescu Approach to Sobolev Spaces
For a function the notion of p-mean variation of order 1, is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space in terms of is directly related to the characterisation of by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.
p-harmonic equation and quasiregular mappings
The Muckenhoupt class A₁(R)
It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.
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