Lp bounds for Riesz transforms and square roots associated to second order elliptic operators.
Lp estimates for singular integrals with kernels beloging to certain block spaces.
We establish the Lp boundedness of singular integrals with kernels which belong to block spaces and are supported by subvarities.
Lp extremal polynomials. Results and perspectives
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...
LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators
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.
Lp multipliers and their H1-L1 estimates on the Heisenberg group.
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.
Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I.
Lp-bounds for spherical maximal operators on Zn.
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...
Lₚ-deviations from zero of polynomials with integral coefficients
Lp-estimates for Oscillatory Integrals in Several Variables.
Lp-Improving Properties for Some Measures Supported on Curves.