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Generalized Hölder estimates for the [기호]-equation on convex domains in ℂ²

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In this paper, we introduce the generalized Hölder space with a majorant function and prove the Hölder regularity for solutions of the Cauchy-Riemann equation in the generalized Hölder spaces on a bounded convex domain in ℂ².

Abstract

In this paper, we introduce the generalized Hölder space with a majorant function and prove the Hölder regularity for solutions of the Cauchy-Riemann equation in the generalized Hölder spaces on a bounded convex domain in ℂ².

참고문헌 (11)

  1. H. Ahn, "Hölder type 1", 2 estimates for the ∂-equation in strictly pseudoconvex domains, 2008, pp.120, 127~138
  2. S. Bloom, "Atomic decomposition of generalized Lipschitz spaces", Illinois J. Math, 33(2), pp.181~209 (1989)
  3. S. Bloom, "Weighted Lipschitz spaces and their analytic characterizations", Constr. Approx, 10(3), pp.339~376 (1994)
  4. K. M. Dyakonov, "Equivalent norms on Lipschitz-type spaces of holomorphic functions", Acta. Math, 178, pp.143~167 (1997)
  5. K. M. Dyakonov, "Holomorphic functions and quasiconformal mappings with smooth moduli", Adv. Math, 187, pp.146~172 (2004)
  6. K. M. Dyakonov, "Strong Hardy-Littlewood theorems for analytic functions and mappings of nite distortion", Math. Z, 249(3), pp.597~611 (2005)
  7. M. Pavlović, "On Dyakonov's paper Equivalent norms on Lipschitz-type spaces of holomorphic functions", Acta. Math, 183, pp.141~143 (1999)
  8. M. Pavlović, "Introduction to Function Spaces on the Disk, Posebna izdanja 20", Mathematički Institut SANU, ~ (2004)
  9. J. C. Polking, "The Cauchy-Riemann equations in convex domains", Proc. Symp. Pure Math, 52, pp.309~322 (1991)
  10. M. Range, "Holomorphic functions and integral representations in several complex variables" (1986), Springer Verlag
  11. M. Range, "On Hölder and BMO estimates for ∂ on convex domains in C2", Journal Geom. Anal, 2(4), pp.575~584 (1992)

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