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arXiv · 2403.14388

Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products

Marc Hovemann
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Abstract

In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univariate boundary adapted quarklets to describe univariate Bessel-Potential spaces on intervals. To obtain the bivariate characterizations a recent result of Hansen and Sickel is applied. It yields that each bivariate Bessel-Potential space on a square can be written as an intersection of function spaces which have a tensor product structure. Hence our main result is a characterization of bivariate Bessel-Potential spaces on squares in terms of quarklets that are tensor products of univariate quarklets on intervals.

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Marc Hovemann. 2024-03-21. Quarklet Characterizations for bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products. https://arxiv.org/abs/2403.14388

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