We investigate L p regularity of weighted Bergman projections on the unit disc and L p regularity of ordinary Bergman projections in higher dimensions.2010 Mathematics Subject Classification. Primary: 32A25, 32A36; Secondary: 32A30.
We prove optimal estimates for the mapping properties of the Bergman projection on the Hartogs triangle in weighted L p spaces when p > 4 3 , where the weight is a power of the distance to the singular boundary point. For 1 < p ā¤ 4 3 we show that no such weighted estimates are possible.2010 Mathematics Subject Classification. 32A25, 32A07.
Abstract. Let M be a pseudoconvex, oriented, bounded and closed CR submanifold of C n of hypersurface type. Our main result says that when a certain 1-form on M is exact on the null space of the Levi form, then the complex Green operator on M satisfies Sobolev estimates. This happens in particular when M admits a set of plurisubharmonic defining functions or when M is strictly pseudoconvex except for the points on a simply connected complex submanifold.
We study the spectrum of the Kohn Laplacian t b on the Rossi example (S 3 , L t ).In particular we show that 0 is in the essential spectrum of t b , which yields another proof of the global non-embeddability of the Rossi example.2010 Mathematics Subject Classification. Primary 32V30; Secondary 32V05.
Proofs of two results about a monomial ideal -describing membership in auxiliary ideals associated to the monomial ideal -are given which do not invoke resolution of singularities. The AM-GM inequality is used as a substitute for taking a log resolution of the monomial ideal.
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