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L p - and S p , q r B -discrepancy of (order 2) digital nets

Lev Markhasin (2015)

Acta Arithmetica

Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the L p -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed...

L p -approximation of Jacobians

Jan Malý (1991)

Commentationes Mathematicae Universitatis Carolinae

The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from Cart p ( Ω , 𝐑 m ) is approximated by 𝒞 1 functions strongly in 𝒜 q ( Ω , 𝐑 m ) whenever q < p . An example is shown of a function which is in cart p ( Ω , 𝐑 2 ) but not in cart p ( Ω , 𝐑 2 ) .

L p -boundedness for pseudodifferential operators with non-smooth symbols and applications

Gianluca Garello, Alessandro Morando (2005)

Bollettino dell'Unione Matematica Italiana

Starting from a general formulation of the characterization by dyadic crowns of Sobolev spaces, the authors give a result of L p continuity for pseudodifferential operators whose symbol a(x,ξ) is non smooth with respect to x and whose derivatives with respect to ξ have a decay of order ρ with 0 < ρ 1 . The algebra property for some classes of weighted Sobolev spaces is proved and an application to multi - quasi - elliptic semilinear equations is given.

L p , q -cohomology of warped cylinders

Yaroslav Kopylov (2009)

Annales mathématiques Blaise Pascal

We extend some results by Gol dshtein, Kuz minov, and Shvedov about the L p -cohomology of warped cylinders to L p , q -cohomology for p q . As an application, we establish some sufficient conditions for the nontriviality of the L p , q -torsion of a surface of revolution.

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