-boundedness of Marcinkiewicz integrals along surfaces with variable kernels: another sufficient condition.
L... maximal estimates for solutions to the Schrödinger equation.
boundedness for the commutator of a homogeneous singular integral operator
The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that is a sufficient condition for the kth order commutator to be bounded on for all 1 < p < ∞. The corresponding maximal operator is also considered.
regularity of velocity averages
weighted inequalities for the dyadic square function
We prove that , where is the dyadic square function, is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.
L2 boundedness of a singular integral operator.
In this paper we study a singular integral operator T with rough kernel. This operator has singularity along sets of the form {x = Q(|y|)y'}, where Q(t) is a polynomial satisfying Q(0) = 0. We prove that T is a bounded operator in the space L2(Rn), n ≥ 2, and this bound is independent of the coefficients of Q(t).We also obtain certain Hardy type inequalities related to this operator.
Limiting case of the boundedness of fractional integral operators on nonhomogeneous space.
Limits of Sequences of Operators on Spaces of Vector Valued Functions.
Linear extension operators for restrictions of function spaces to irregular open sets
Lipschitz estimates for multilinear commutator of Littlewood-Paley operator.
Lipschitz estimates for multilinear commutator of pseudo-differential operators.
Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups
We give a characterization of the Hölder-Zygmund spaces () on a stratified Lie group in terms of Littlewood-Paley type decompositions, in analogy to the well-known characterization of the Euclidean case. Such decompositions are defined via the spectral measure of a sub-Laplacian on , in place of the Fourier transform in the classical setting. Our approach mainly relies on almost orthogonality estimates and can be used to study other function spaces such as Besov and Triebel-Lizorkin spaces...
Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets
Let be a closed null set. We prove an equivalence between the Littlewood-Paley decomposition in with respect to the complementary intervals of and Fourier multipliers of Hörmander-Mihlin and Marcinkiewicz type with singularities on . Similar properties are studied in for a union of rays from the origin. Then there are connections with the maximal function operator with respect to all rectangles parallel to these rays. In particular, this maximal operator is proved to be bounded on , ,...
Littlewood-Paley decompositions on manifolds with ends
For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) spaces, using the usual square function defined by a dyadic partition.
Littlewood-Paley -function in the Dunkl analysis on .
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.