[Les espaces de Besov et les projections de Bergman dans la boule]
Nous étudions une class d'opérateurs différentiels radiaux conduisant à une classification naturelle des espaces de Besov diagonaux dans la boule unité de . Nous donnons les conditions précises pour la bornitude des projections de Bergman de certains espaces Lp sur des espaces de Besov. Nous déterminons aussi des inverses à droite pour ces projections. Nous présentons des applications à l'interpolation complexe.
A class of radial differential operators are investigated yielding a natural classification of diagonal Besov spaces on the unit ball of . Precise conditions are given for the boundedness of Bergman projections from certain Lp spaces onto Besov spaces. Right inverses for these projections are also provided. Applications to complex interpolation are presented.
Accepté le :
Publié le :
H.Turgay Kaptanoğlu 1
@article{CRMATH_2002__335_9_729_0, author = {H.Turgay Kaptano\u{g}lu}, title = {Besov spaces and {Bergman} projections on the ball}, journal = {Comptes Rendus. Math\'ematique}, pages = {729--732}, publisher = {Elsevier}, volume = {335}, number = {9}, year = {2002}, doi = {10.1016/S1631-073X(02)02556-6}, language = {en}, }
H.Turgay Kaptanoğlu. Besov spaces and Bergman projections on the ball. Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 729-732. doi : 10.1016/S1631-073X(02)02556-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02556-6/
[1] Complete Nevanlinna–Pick kernels, J. Funct. Anal., Volume 175 (2000), pp. 111-124
[2] Integral formulas for a sub-Hardy Hilbert space on the ball with complete Nevanlinna–Pick reproducing kernel, C. R. Acad. Sci. Paris, Série I, Volume 333 (2001), pp. 285-290
[3] Some-finite dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem, Integral Equations Operator Theory, Volume 42 (2002), pp. 1-21
[4] D. Alpay, H.T. Kaptanoğlu, Gleason's problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball, J. Math. Anal. Appl., 2002, to appear
[5] Boundedness and compactness of generalized Hankel operators on bounded symmetric domains, J. Funct. Anal., Volume 137 (1996), pp. 97-151
[6] Membership of Hankel operators on the ball in unitary ideals, J. London Math. Soc., Volume 43 (1991), pp. 485-508
[7] Invariant inner product in spaces of holomorphic functions on bounded symmetric domains, Doc. Math., Volume 2 (1997), pp. 213-261
[8] Interpolation and commutant lifting for multipliers on reproducing kernel Hilbert spaces, Oper. Theory Adv. Appl., 122, Birkhäuser, Basel, 2001, pp. 89-138
[9] Holomorphic Sobolev spaces on the ball, Dissertationes Math., Volume 276 (1989)
[10] Möbius invariant Besov p-spaces and Hankel operators in the Bergman space on the ball in , Complex Variables Theory Appl., Volume 17 (1991), pp. 89-104
[11] Möbius invariant spaces on the unit ball, Michigan Math. J., Volume 39 (1992), pp. 509-536
[12] Tangential limits and exceptional sets for holomorphic Besov functions in the unit ball of , Illinois J. Math., Volume 37 (1993), pp. 171-185
[13] Invariant differential operators and holomorphic function spaces, J. Lie Theory, Volume 10 (2000), pp. 1-31
[14] Operator Theory in Function Spaces, Dekker, New York, 1990
[15] Holomorphic Besov spaces on bounded symmetric domains, I, Quart. J. Math. Oxford, Volume 46 (1995), pp. 239-256
[16] Holomorphic Besov spaces on bounded symmetric domains, II, Indiana Univ. Math. J., Volume 44 (1995), pp. 1017-1031
Cité par Sources :
Commentaires - Politique