Zobrazeno 1 - 10
of 128
pro vyhledávání: '"McNeal, A. D."'
Autor:
Chen, Liwei, McNeal, Jeffery D.
Solution operators for the equation $\bar \partial u=f$ are constructed on general product domains in $\mathbb{C}^n$. When the factors are one-dimensional, the operator is a simple integral operator: it involves specific derivatives of $f$ integrated
Externí odkaz:
http://arxiv.org/abs/1904.09401
Autor:
Edholm, L. D., McNeal, J. D.
Publikováno v:
J. Geom. Anal. 30 (2020), no. 2, 1293-1311
Sobolev irregularity of the Bergman projection on a family of domains containing the Hartogs triangle is shown. On the Hartogs triangle itself, a sub-Bergman projection is shown to satisfy better Sobolev norm estimates than its Bergman projection.
Externí odkaz:
http://arxiv.org/abs/1904.04383
Publikováno v:
Adv. Math. 341 (2019), 616-656
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are pro
Externí odkaz:
http://arxiv.org/abs/1804.02746
Autor:
McNeal, J. D., Xiong, J.
A classical observation of Riesz says that truncations of a general $\sum_{n=0}^\infty a_n z^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman norm $A^1$. T
Externí odkaz:
http://arxiv.org/abs/1803.10822
Autor:
McNeal, Jeffery D., Mernik, Luka
The singular and regular type of a point on a real hypersurface $\mathcal H$ in $\mathbb C^n$ are shown to agree when the regular type is strictly less than 4. If $\mathcal H$ is pseudoconvex, we show they agree when the regular type is 4. A non-pseu
Externí odkaz:
http://arxiv.org/abs/1708.02673
Autor:
McNeal, Jeffery D., Varolin, Dror
We study the problem of extension of normal jets from a hypersurface, with focus on the growth order of the constant. Using aspects of the standard, twisted approach for $L^2$ extension and of the new approach to $L^2$ extension introduced by Berndts
Externí odkaz:
http://arxiv.org/abs/1707.04483
Autor:
Edholm, L. D., McNeal, J. D.
Publikováno v:
J Geom Anal (2017) 27: 2658-2683
Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $\gamma$. A surprising consequence of the analysis is that, when
Externí odkaz:
http://arxiv.org/abs/1605.06223
Autor:
McNeal, Jeffery D., Varolin, Dror
We establish $L^2$ extension theorems for $\bar \partial$-closed $(0,q)$-forms with values in a holomorphic line bundle with smooth Hermitian metric, from a smooth hypersurface on a Stein manifold. Our result extends (and gives a new, perhaps more cl
Externí odkaz:
http://arxiv.org/abs/1502.08054
Autor:
McNeal, Jeffery D., Varolin, Dror
This is a survey article about $L^2$ estimates for the $\bar \partial$ operator. After a review of the basic approach that has come to be called the "Bochner-Kodaira Technique", the focus is on twisted techniques and their applications to estimates f
Externí odkaz:
http://arxiv.org/abs/1502.08047
Autor:
Edholm, L. D., McNeal, J. D.
Publikováno v:
Proc. Amer. Math. Soc. 144 (2016), 2185-2196
A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the "fatness"
Externí odkaz:
http://arxiv.org/abs/1502.07302