Littlewood-Paley operators on the generalized Lipschitz spaces.
Littlewood-Paley-Stein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2
We study the weak type (1,1) and the -boundedness, 1 < p ≤ 2, of the so-called vertical (i.e. involving space derivatives) Littlewood-Paley-Stein functions and ℋ respectively associated with the Poisson semigroup and the heat semigroup on a complete Riemannian manifold M. Without any assumption on M, we observe that and ℋ are bounded in , 1 < p ≤ 2. We also consider modified Littlewood-Paley-Stein functions that take into account the positivity of the bottom of the spectrum. Assuming that...
Littlewood-Paley-Stein theory for semigroups in UMD spaces.
Littlewood-Paley-Stein theory on Cn and Weyl multipliers.
Local Field Singular Integrals with Complex Homogeneity.
Local integrability of strong and iterated maximal functions
Let denote the strong maximal operator. Let and denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that but . It is shown that if f is a function supported on Q such that but , then there exists a set A of finite measure in ℝ² such that .
Local means and wavelets in function spaces
The paper deals with local means and wavelet bases in weighted and unweighted function spaces of type and on ℝⁿ and on ⁿ.
Local properties of Fourier series.
Local Riesz transform characterization of local Hardy spaces
Local Theorems for the Absolute Convergence of Multiple Lacunary Fourier Series.
Localization and Convergence of Eigenfunction Expansions.
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 .
Logarithmic Sobolev inequalitites and the existence of singular integrals.
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 → 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...