A note on the diagonal mapping in spaces of analytic functions in the unit polydisc

• Autores: Miroljub Jevtic, Miroslav Pavlovic, Romi F. Shamoyan
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 74, Fasc. 1-2, 2009, págs. 45-58
• Idioma: inglés
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• Resumen

  • We de¯ne two spaces Kp;q;®;¯ and Mp;® of analytic functions in the unit polydisc Un of Cn, closely related to the mixed norm and the Bergman spaces on Un, and for any holomorphic function F in Kp;q;®;¯ or in Mp;® we consider its restriction to the diagonal, i.e., the function in the unit disc U of C de¯ned by DF(z) = F(z; : : : ; z), and prove that the diagonal mapping D maps Kp;q;®;¯ onto the mixed-norm space Hp;q;¯+q p (j®j+2n¡1)(U) and the space Mp;® onto the Bergman space Ap;j®j+2n¡1(U).