Displaying similar documents to “Remarks on the Hilbert transform and on some families of multiplier operators related to it.”

Families of reduced zero-dimensional schemes.

Juan C. Migliore (2006)

Collectanea Mathematica

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A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the...

Rough Marcinkiewicz integral operators on product spaces.

Hussein M. Al-Qassem (2005)

Collectanea Mathematica

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In this paper, we study the Marcinkiewicz integral operators M on the product space R x R. We prove that M is bounded on L(R x R) (1< p < ∞) provided that h is a bounded radial function and Ω is a function in certain block space B (S x S) for some q > 1. We also establish the optimality of our condition in the sense that the space B (S x S) cannot be replaced by B (S x S) for any −1 < r < 0. Our results...

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.