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By Boris Nikolaevič Apanasov (auth.), Julian Ławrynowicz (eds.)

ISBN-10: 3540127127

ISBN-13: 9783540127123

ISBN-10: 3540386971

ISBN-13: 9783540386971

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Additional info for Analytic Functions Błażejewko 1982: Proceedings of a Conference held in Błażejewko, Poland, August 19–27, 1982

Example text

As for the existence of a strongly continuous extension l 2 it is sufficient to show that ToC') is strongly uniformly continuous on the T('), intersection of Let Po Do with the closure P0 of any polydisk P0 be such a polydisk and consider another polydisl< P, such that PoC: Do' PCP c: D with 0 po() a0 P=0, where a0 P is the distinguished boundary of P. Now, as k(·,·) sesqui-holomorphic on DXD, ke:H(DxD). eP. for for every dz=dzl ••• dz n J f 1 k(Z,1;)dzd~ (Z-W) ('1;-1') a PdP o 0 Here we have also used the multinomial abbreviation of z"'(zl, ••• ,zn)e~n.

J. 4 (1981), 495-507. : Operator-valued Pick's conditions and holomorphicity, Pacific J. Math. 98 (1982), 295-311. : Monotone MatriX Functions and Analytic Continuation, SpringerVerlag, New York, 1974. : On quadratic and bilinear forms in function theory, Proc. London Math. Soc. (3) 44 (1982), 554-576. : 527-531. Pick's conditions and analyticity, Pacific J. Math. A. ABOUT THE EQUALITY BETWEEN THE p-MODULE AND THE p-CAPACITY IN an Petru Caraman .. ~w, Contents Introduction ,. p-module and p-~apa~i ty' i~ the ~a;e' of ;p~n' s~t; • D~ n ' 2.

P-module and p-capacity of topological cylinders • • . • 4. Historical remarks . • • . • . • • . • • • • 5. Evaluation of an exceptional set for quasiconformal mappings • • • • • • • • References • • • • • • • • • • • • • • • • R 32 33 66 67 71 79 82 Introduction In this paper, we establish that , wnere D '~s an open set ~n . th e Euc lidean n-space Rn, Eo' E1 eRn are two sets such that the distance d (Eo ,E ) > 0 and Eo n 3D or El n aD 1 (aD = the boundary of D) satisfies some additional conditions, r(Eo,E"D) is the family of arcs joining Eo and El in D, Mpr is the p-module of an arc family r, and cap (E ,E"D) is the p-capacity p 0 of Eo,E, relative to D.

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Analytic Functions Błażejewko 1982: Proceedings of a Conference held in Błażejewko, Poland, August 19–27, 1982 by Boris Nikolaevič Apanasov (auth.), Julian Ławrynowicz (eds.)


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