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Displaying 1461 –
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Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Koifman, Meyer and Wickerhauser that many wavelet packets wn suffer a lack of frequency localization. Using the L1-norm of the Fourier transform ^wn as localization criterion, they showed that the average 2-jΣn=02j-1 ||^wn||L1 blows up as j goes to infinity. A natural problem is then to know which values of n create this blow-up in average. The present work gives an answer to this question,...
We study logarithmic estimates for a class of Fourier multipliers which arise from a nonsymmetric modulation of jumps of Lévy processes. In particular, this leads to corresponding tight bounds for second-order Riesz transforms on .
We establish the Lp boundedness of singular integrals with kernels which belong to block spaces and are supported by subvarities.
2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.Let α = β+γ be a positive finite measure defined on the Borel sets of C, with compact support, where β is a measure concentrated on a closed Jordan curve or on an arc (a circle or a segment) and γ is a discrete measure concentrated on an infinite number of points.
In this survey paper, we present a synthesis on the asymptotic behaviour of orthogonal polynomials or Lp extremal polynomials associated to the measure α. We analyze...
Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given.* This paper has been supported by Russian Fond of Fundamental Investigations under Grant No. 40–01–008632 a.
We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.
We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a...
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