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Lebesgue measure and mappings of the Sobolev class W 1 , n

O. Martio (1995)

Banach Center Publications

We present a survey of the Lusin condition (N) for W 1 , n -Sobolev mappings f : G n defined in a domain G of n . Applications to the boundary behavior of conformal mappings are discussed.

Lebesgue points for Sobolev functions on metric spaces.

Juha Kinnunen, Visa Latvala (2002)

Revista Matemática Iberoamericana

Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation...

Left quotients of a C*-algebra, III: Operators on left quotients

Lawrence G. Brown, Ngai-Ching Wong (2013)

Studia Mathematica

Let L be a norm closed left ideal of a C*-algebra A. Then the left quotient A/L is a left A-module. In this paper, we shall implement Tomita’s idea about representing elements of A as left multiplications: π p ( a ) ( b + L ) = a b + L . A complete characterization of bounded endomorphisms of the A-module A/L is given. The double commutant π p ( A ) ' ' of π p ( A ) in B(A/L) is described. Density theorems of von Neumann and Kaplansky type are obtained. Finally, a comprehensive study of relative multipliers of A is carried out.

Left-covariant differential calculi on S L q ( N )

Konrad Schmüdgen, Axel Schüler (1997)

Banach Center Publications

We study N 2 - 1 dimensional left-covariant differential calculi on the quantum group S L q ( N ) . In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus. It turns out...

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