Tangential boundary behavior of functions of several variables
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In this paper we study the asymptotic behavior of functions defined on domains of a multidimensional real or complex space when the point tends to the boundary in the approach region with different orders of tangency. The main results are related to the boundary behavior of functions from Hardy-Sobolev spaces in a multidimensional complex ball and of solutions to elliptic boundary-value problems in a Lipschitz domain of a real Euclidean space. The methods used are based on two-weighted estimates for tangential maximal functions in an abstract ball. The boundary of this ball is a space equipped with measure and quasimetric.
Key wordstangential boundary behavior Hardy-Sobolev space elliptic boundary-value problem Dirichlet problem two-weighted estimate
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