Estimations höldériennes pour les equations de Cauchy-Riemann dans les convexes compacts de ℂ n

Chaumat, Jacques; Chollet, Anne-Marie

doi:10.1007/bf02571405

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…Finally, we should mention that Chaumat and Chollet [10] obtained a ∂ solution with a loss of n − q − 1 derivatives, when D is a convex domain of C 2 boundary and r ∈ N. They also obtained other results. Michel-Shaw [43] also showed that when D is an annulus domain 1 \ 2 , where 1 is a bounded strictly pseudoconvex domain with C ∞ boundary, 2 is a pseudoconvex domain which is relatively compact in 1 and has C 2 boundary, there exists a solution u ∈…”

Section: Introductionmentioning

confidence: 87%

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $$C^2$$ C 2 boundary

Gong

2018

Math. Ann.

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We derive a new homotopy formula for a strictly pseudoconvex domain of C 2 boundary in C n by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators. For r > 1 and q > 0, we obtain a r +1/2 solution u to ∂u = f for a ∂-closed (0, q)-form f of class r in the domain. We apply the estimates to obtain boundary regularities of D-solutions for a domain inthat admits a derivative estimate. Here ϕ is a (0, q)-form in D and ϕ, ∂ϕ are in C 1 (D). We will prove the following C r +1/2 estimate. Communicated by Ngaiming Mok.

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Section: Introductionmentioning

confidence: 87%

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $$C^2$$ C 2 boundary

Gong

2018

Math. Ann.

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“…The corresponding problem for pseudoconvex domains is unsolved except for s-H-convex domains, cf. [2,3,4]. The resulting loss of regularity is far from being minimal even with our methods.…”

Section: Remarkmentioning

confidence: 99%

A decomposition problem on weakly pseudoconvex domains

Michel

Shaw

1999

Math Z

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“…Finally, we should mention that Chaumat and Chollet [10] obtained a ∂ solution with a loss of n − q − 1 derivatives, when D is a convex domain of C 2 boundary and r ∈ N. They also obtained other results. Michel-Shaw [43] also showed that when D is an annulus domain Ω 1 \ Ω 2 , where Ω 1 is a bounded strictly pseudoconvex domain with C ∞ boundary, Ω 2 is a pseudoconvex domain which is relatively compact in Ω 1 and has C 2 boundary, there exists…”

Section: Introductionmentioning

confidence: 87%

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $C^2$ boundary

Gong

2017

Preprint

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We derive a new homotopy formula for a strictly pseudoconvex domain of C 2 boundary in C n by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators. For r > 1 and q > 0, we obtain a Λ r+1/2 solution u to ∂u = f for a ∂-closed (0, q)-form f of class Λ r in the domain. We apply the estimates to obtain boundary regularities of D-solutions for a domain in C n × R m .

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Estimations höldériennes pour les equations de Cauchy-Riemann dans les convexes compacts de ℂ n

Cited by 7 publications

References 7 publications

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $$C^2$$ C 2 boundary

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $$C^2$$ C 2 boundary

A decomposition problem on weakly pseudoconvex domains

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $C^2$ boundary

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