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Zeitschrift für Analysis und ihre Anwendungen


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Volume 1, Issue 6, 1982, pp. 1–16
DOI: 10.4171/ZAA/37

Published online: 1982-12-31

Extremal inequalities in Sobolev spaces and quasiconformal mappings

Tadeusz Iwaniec[1]

(1) University of Warsaw, Poland

We estimate the norm of a two-dimensional Hilbert operator in $L_p-spaces. This problen leads to inequalities of the theory of Sobolev spaces. In certain cases, by using methods of the theory of quasiconformal mappings, we get best possible estimates.

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Iwaniec Tadeusz: Extremal inequalities in Sobolev spaces and quasiconformal mappings. Z. Anal. Anwend. 1 (1982), 1-16. doi: 10.4171/ZAA/37