We prove that classical Coifman-Meyer theorem holds on any polidisc Td or arbitrary dimension d ≥ 1.

Extension by integer translates of compactly supported function for multiplier spaces on periodic Hardy spaces to multiplier spaces on Hardy spaces is given. Shannon sampling theorem is extended to Hardy spaces.

The author proves the boundedness for a class of multiplier operators on product spaces. This extends a result obtained by Lung-Kee Chen in 1994.

The authors obtain some multiplier theorems on $H^p$ spaces analogous to the classical $L^p$ multiplier theorems of de Leeuw. The main result is that a multiplier operator ${\left(Tf\right)}^{(}x)=\lambda \left(x\right)f̂\left(x\right)$$(\lambda \in C(...$

We study multipliers M (bounded operators commuting with translations) on weighted spaces L ω p (ℝ), and establish the existence of a symbol µM for M, and some spectral results for translations S t and multipliers. We also study operators T on the weighted space L ω p (ℝ+) commuting either with the right translations S t , t ∈ ℝ+, or left translations P +S −t , t ∈ ℝ+, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ(S t ) of the operator S t proving that...

The aim of this paper is to prove certain multiplier theorems for the Hermite series.

We study $¹-L^p$ boundedness of certain multiplier transforms associated to the special Hermite operator.

We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix ${\left(\phi (i+j)\right)}_{i,j\ge 0}$ is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call “shift-bounded”. We show that there is a φ which is a “completely...

Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators are studied. We prove that $L^p$-uniform, 1 < p < ∞, spectral multipliers extend to holomorphic functions in some subset of a polysector, depending on p. We also characterize L¹-uniform spectral multipliers and prove a Marcinkiewicz-type multiplier theorem. In the appendix we obtain analogous results for systems of Laguerre operators.

Let $C{V}_p\left(F\right)$ be the left convolution operators on $L^p\left(G\right)$ with support included in F and $M_p\left(F\right)$ denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that $C{V}_p\left(F\right)$, $C{V}_p\left(F\right)/M_p\left(F\right)$ and $C{V}_p\left(F\right)/W$ are as big as they can be, namely have $l^{\infty }$ as a quotient, where the ergodic space W contains, and at times is very big relative to $M_p\left(F\right)$. Other subspaces of $C{V}_p\left(F\right)$ are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

For the convolution operators $A_a^{\alpha }$ with symbols ${a\left(\right|\xi \left|\right)\left|\xi \right|}^{-\alpha }expi\left|\xi \right|$, 0 ≤ Re α < n, $a\left(\right|\xi \left|\right)\in L_{\infty }$, we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from $L_p$ to $L_q$.

We study different discrete versions of maximal operators and g-functions arising from a convolution operator on R. This allows us, in particular, to complete connections with the results of de Leeuw [L] and Kenig and Tomas [KT] in the setting of the groups R^{N}, T^{N} and Z^{N}.

We investigate the $L^p$ boundedness for a class of parametric Marcinkiewicz integral operators associated to submanifolds and a class of related maximal operators under the $L{\left(logL\right)}^{\alpha }{(}^{n-1})$ condition on the kernel functions. Our results improve and extend some known results.