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1999 | 134 | 3 | 269-298
Tytuł artykułu

Convergence in nonisotropic regions of harmonic functions in $𝔹^n$

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the boundedness in $L^p(𝕊^n)$ of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in $L^p(𝕊^n)$ with spectrum included in these horizontal strips.
Czasopismo
Rocznik
Tom
134
Numer
3
Strony
269-298
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-10-14
poprawiono
1998-11-10
Twórcy
  • Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain, cascante@cerber.mat.ub.es
  • Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain, ortega@cerber.mat.ub.es
Bibliografia
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  • [BoCl] A. Bonami et J.-L. Clerc, Sommes de Cesàro et multiplicateurs des développements en harmoniques sphériques, Trans. Amer. Math. Soc. 183 (1973), 223-263.
  • [BrCa] J. Bruna and C. Cascante, Restriction to transverse curves of some spaces of functions in the unit ball, Michigan Math. J. 36 (1989), 387-401.
  • [BrOr] J. Bruna and J. M. Ortega, Closed finitely generated ideals in algebras of holomorphic functions and smooth to the boundary in strictly pseudoconvex domains, Math. Ann. 268 (1984), 137-157.
  • [CaOr] C. Cascante and J. M. Ortega, A characterisation of tangential exceptional sets for $H_α^p$, α p=n, Proc. Roy. Soc. Edinburgh 126 (1996), 625-641.
  • [Ch] E. M. Chirka, The Lindelöf and Fatou theorems in $ℂ^n$, Mat. Sb. 92 (1973), 622-644 (in Russian).
  • [Do] E. Doubtsov, thesis, Université Bordeaux I, 1995.
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  • [Kr2] V. G. Krotov, A sharp estimate of the boundary behavior of functions in the Hardy-Sobolev classes $H_α^p(𝔹^n)$ in the critical case α p=n, Dokl. Akad. Nauk SSSR 319 (1991), 42-45 (in Russian); English transl.: Soviet Math. Dokl. 44 (1992), 36-39.
  • [Li] E. Lindelöf, Sur un principe générale de l'analyse et ses applications à la théorie de la représentation conforme, Acta Soc. Sci. Fenn. 46 (1915), 1-35.
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  • [NaRu] A. Nagel and W. Rudin, Local boundary behavior of bounded holomorphic functions, Canad. J. Math. 30 (1978), 583-592.
  • [NaRuSh] A. Nagel, W. Rudin and J. H. Shapiro, Tangential boundary behavior of functions in Dirichlet-type spaces, Ann. of Math. 116 (1982), 331-360.
  • [NaWa] A. Nagel and S. Wainger, Limits of bounded holomorphic functions along curves, in: Recent Developments in Several Complex Variables, J. E. Fornaess (ed.), Princeton Univ. Press, 1981, 327-344.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv134i3p269bwm
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