133,583 research outputs found

    Littlewood-Paley-Stein type square functions based on Laguerre semigroups

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    We investigate g-functions based on semigroups related to multi-dimensional Laguerre function expansions of convolution type. We prove that these operators can be viewed as Calderon-Zygmund operators in the sense of the underlying space of homogeneous type, hence their mapping properties follow from the general theory.Comment: 30 page

    Transcendence measures and algebraic growth of entire functions

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    In this paper we obtain estimates for certain transcendence measures of an entire function ff. Using these estimates, we prove Bernstein, doubling and Markov inequalities for a polynomial P(z,w)P(z,w) in C2{\Bbb C}^2 along the graph of ff. These inequalities provide, in turn, estimates for the number of zeros of the function P(z,f(z))P(z,f(z)) in the disk of radius rr, in terms of the degree of PP and of rr. Our estimates hold for arbitrary entire functions ff of finite order, and for a subsequence {nj}\{n_j\} of degrees of polynomials. But for special classes of functions, including the Riemann ζ\zeta-function, they hold for all degrees and are asymptotically best possible. From this theory we derive lower estimates for a certain algebraic measure of a set of values f(E)f(E), in terms of the size of the set EE.Comment: 40 page

    Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index

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    In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.Comment: 40 page
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