L... - L... Estimates for Convolution Operators with n-Dimensional Singular Measures.
-improving properties for measures on supported on homogeneous surfaces in some non elliptic cases.
-multipliers for the Laguerre expansions
regularity of velocity averages
spectral multipliers on the free group
Let L be a homogeneous sublaplacian on the 6-dimensional free 2-step nilpotent Lie group on three generators. We prove a theorem of Mikhlin-Hörmander type for the functional calculus of L, where the order of differentiability s > 6/2 is required on the multiplier.
Littlewood-Paley-Stein theory on Cn and Weyl multipliers.
Local properties of Fourier series.
Localization of factored Fourier series.
Logarithmic inequalities for second-order Riesz transforms and related Fourier multipliers
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 .
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 → 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-estimates for Oscillatory Integrals in Several Variables.
Lp-Improving Properties for Some Measures Supported on Curves.