In this paper we obtain several characterizations of the pointwise multipliers of the space in the unit ball of . Moreover, if are holomorphic functions on , we prove that maps onto if and only if the functions are multipliers of the space and satisfy
Dans cet article nous obtenons plusieurs caractérisations des multiplicateurs ponctuels de l’espace dans la boule unité de . De plus, si sont des fonctions holomorphes dans nous démontrons que l’application envoie sur si et seulement si les fonctions sont multiplicateurs de l’espace et satisfont
@article{AIF_1996__46_1_111_0, author = {Ortega, J. M. and F\`abrega, Joan}, title = {Pointwise multipliers and corona type decomposition in $BMOA$}, journal = {Annales de l'Institut Fourier}, pages = {111--137}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {1}, year = {1996}, doi = {10.5802/aif.1509}, zbl = {0840.32001}, mrnumber = {97k:32009}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1509/} }
TY - JOUR AU - Ortega, J. M. AU - Fàbrega, Joan TI - Pointwise multipliers and corona type decomposition in $BMOA$ JO - Annales de l'Institut Fourier PY - 1996 SP - 111 EP - 137 VL - 46 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1509/ DO - 10.5802/aif.1509 LA - en ID - AIF_1996__46_1_111_0 ER -
%0 Journal Article %A Ortega, J. M. %A Fàbrega, Joan %T Pointwise multipliers and corona type decomposition in $BMOA$ %J Annales de l'Institut Fourier %D 1996 %P 111-137 %V 46 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1509/ %R 10.5802/aif.1509 %G en %F AIF_1996__46_1_111_0
Ortega, J. M.; Fàbrega, Joan. Pointwise multipliers and corona type decomposition in $BMOA$. Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 111-137. doi : 10.5802/aif.1509. https://aif.centre-mersenne.org/articles/10.5802/aif.1509/
[A] On the corona theorem., J. of Geom. Anal., 1 (1991), 291-305. | MR | Zbl
,[AB] Mesures de Carleson d'ordre α et estimations de solutions du ∂, BSM France, 107 (1979), 23-48. | EuDML | Numdam | MR | Zbl
, ,[An] On the Hp-corona problem, Bull. Sci. Math., 118 (1994), 287-306. | MR | Zbl
,[AnCa1] Wolff-type estimates and the Hp-corona problem in strictly pseudoconvex domains, Ark. Mat., 32 (1994), 255-276. | MR | Zbl
, ,[AnCa2] Hp-estimates of holomorphic division formulas, Preprint. | Zbl
, ,[AxSh] Putnam's theorem, Alexander's spectral area estimate and VMO, Math. Ann., 271 (1985), 161-183. | EuDML | MR | Zbl
, ,[B] A formula for division and interpolation, Math. Ann., 263 (1983), 399-418. | EuDML | MR | Zbl
,[BAn] Henkin-Ramirez formulas with weight factors, Ann. Inst. Fourier (Grenoble), 32-3 (1983), 91-110. | EuDML | Numdam | MR | Zbl
, ,[BrBu] Holomorphic Approximation in Cm-Norms on Totally Real Compact Sets in ℂn, Math. Ann., 269 (1984), 103-117. | EuDML | MR | Zbl
, ,[C] Interpolation by bounded analytic functions and the corona theorem, Ann. of Math., 76 (1962), 547-559. | MR | Zbl
,[Ch] Solutions minimales de l'équation ∂u = f dans la boule et le polydisque, Ann. Inst. Fourier (Grenoble), 30-4 (1980), 121-153. | Numdam | MR | Zbl
,[Chee] VMOA and vanishing Carleson measures, Complex Variables Theory and Appl., 25 (1994), 311-322. | MR | Zbl
,[ChoaChoe] A Littlewwod-Paley type identity and a characterization of BMOA, Complex Variables Theory and Appl., 17 (1991), 15-23. | MR | Zbl
, ,[CoRoW] Factorization theorems in Hardy spaces in several variables, Ann. of Math., 103 (1976), 611-645. | MR | Zbl
, , ,[CoW] Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., 83 (1977), 569-645. | MR | Zbl
, ,[Cu] Extension holomorphe dans des classes de Hardy et estimations de type mesures de Carleson pour ∂u = f, Ann. Inst. Fourier, 33-3 (1983), 59-97. | Numdam | MR | Zbl
,[G] Bounded Analytic Functions, Academic Press, Orlando, Fla., 1981. | MR | Zbl
,[H] An introduction to complex analysis in several variables, Van Nostram, Princeton, 1966. | MR | Zbl
,[J] A note on the Carleson measure characterization of BMOA functions on the unit ball, Complex Variables Theory and Appl., 25 (1992), 189-194. | MR | Zbl
,[Li] Corona problem of several complex variables, Contemporary Math., 137 (1992), 307-328. | MR | Zbl
,[Lin] Hp solutions for the corona problem on the polidisc of ℂn, Bull. A.M.S., 110 (1986), 69-84. | MR | Zbl
,[MS] Theory of multipliers in spaces of differentiable functions, Pitmann, 1985. | Zbl
, ,[N] The corona property for bounded analytic functions in some Besov spaces, Proc. Amer. Math. Soc., 110 (1990), 135-140. | MR | Zbl
,[OF] Corona type decomposition in some Besov spaces, to appear in Math. Scand. | Zbl
, ,[R] Function theory in the unit ball of ℂn, Springer-Verlag, New York, 1980. | MR | Zbl
,[Sa] Function theory in the unit circle, Virginia Poly. Inst. and St. Univ., Backburg, VA, 1979. | Zbl
,[Sh] Cluster sets, essential range and distance estimates in BMO, Mich. Math. J., 34 (1987), 323-335. | MR | Zbl
,[S] Bounded toeplitz operators on H1 and application of the duality between H1 and the functions of Bounded Mean Oscilation, Amer. J. Math., 98 (1976), 573-589. | MR | Zbl
,[T] The corona theorem in algebras of bounded analytic functions, Amer. Math. Soc. Trans., 149 (1991), 61-93. | Zbl
,[V1] BMO functions and the ∂-equation, Pacific J. Math., 71 (1977), 221-273. | MR | Zbl
,[V2] Zeros of Hp functions in several complex variables, Pacific J. Math., 88 (1980), 189-246. | MR | Zbl
,[Z] Multipliers of BMO in the Bergman metric with applications to Toeplitz operators, J. Functional Anal., 87 (1989), 31-50. | MR | Zbl
,Cited by Sources: