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BERGMAN KERNEL ESTIMATES FOR GENERALIZED FOCK SPACES

박수현|조홍래
영남수학회 (Youngnam Mathematical Society)|2017.01|East Asian Mathematical Journal|제33권 제1호|pp. 37-44|DOI http://dx.doi.org/10.7858/eamj.2017.004

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참고문헌

키워드

Bergman kernelgeneralized Fock spaceexponential type weight
주제분류수학

초록

We will prove size estimates of the Bergman kernel for the generalized Fock space Fφ2, where φ belongs to the class W. The main tool for the proof is to use the estimate on the canonical solution to the ∂ ̄-equation. We use Delin’s weighted L2-estimate ([3], [6]) for it.

Abstract

We will prove size estimates of the Bergman kernel for the generalized Fock space Fφ2, where φ belongs to the class W. The main tool for the proof is to use the estimate on the canonical solution to the ∂ ̄-equation. We use Delin’s weighted L2-estimate ([3], [6]) for it.

참고문헌 (10)

  1. H. Arroussi, "Reproducing kernel estimates, bounded projections and duality on large weighted Bergman spaces", J. Geom. Anal, 25(4), pp.2284~2312 (2015)
  2. S. Asserda, "Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights", C. R. Acad. Sci. Paris, Ser. I, 352(1), pp.13~16 (2014)
  3. B. Berndtsson, "Weighted estimates for the ∂-equation, Complex analysis and geometry (Columbus, OH, 1999)", Ohio State Univ. Math. Res. Inst. Publ, 9, pp.43~57 (1999)
  4. O. Constantin, "Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces", J. Geom. Anal, 26(2), pp.1109~1154 (2016)
  5. M.-O. Czarnecki, "Approximation and regularization of Lipschitz functions:convergence of the gradients", Trans. Amer. Math. Soc, 358(10), pp.4467~4520 (2006)
  6. H. Delin, "Pointwise estimates for the weighted Bergman projection kernel in Cn using a weighted L2 estimate for the @ equation", Ann. Inst. Fourier (Grenoble), 48(4), pp.967~997 (1998)
  7. P. Lin, "Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights", Pacific J. Math, 173(1), pp.127~146 (1996)
  8. N. Marco, "Intepolation and sampling sequence for entire functions", Geom. Funct. Anal, 13, pp.862~914 (2003)
  9. J. Marzo, "Pointwise estimates for the Bergman kernel of the weighted Fock space", J. Geom. Anal, 19, pp.890~910 (2009)
  10. M. Pavlovic, "An equivalence for weighted integrals of an analytic func-tion and its derivative", Math. Nachr, 281, pp.1612~1623 (2008)

관련 논문AI추천

SOME REMARKS ON EXTREMAL PROBLEMS IN WEIGHTED BERGMAN SPACES OF ANALYTIC FUNCTIONS이현호, Milos Arsenovic, Romi F. Shamoyan대한수학회 · 대한수학회논문집2012 · 제27권 제4호SOME NEW CHARACTERIZATIONS OF WEIGHTED BERGMAN SPACESSongxiao Li대한수학회 · 대한수학회보2010 · 제47권 제6호Lp-boundedness (1 ≤ p ≤ ∞) for Bergman Projection on a Class of Convex Domains of Infinite Type in C2Ly Kim Ha경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제3호Estimates of the Bergman kernel function on pseudoconvex domains with comparable Levi form조상현대한수학회 · 대한수학회지2002 · 제39권 제3호Remarks on weighted harmonic Bergman functions on half-spaces이흥수장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제3호Weighted Harmonic Bergman functions on Half-Spaces구형운, 남계숙, 이흥수대한수학회 · 대한수학회지2005 · 제42권 제5호

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