Related papers: BMO spaces associated with semigroups of operators

We study tent spaces on general measure spaces $(\Omega, \mu)$. We assume that there exists a semigroup of positive operators on $L^p(\Omega, \mu)$ satisfying a monotone property but do not assume any geometric/metric structure on $\Omega$.…

In this paper we establish the $L^p$-$L^q$ boundedness of Fourier multipliers on locally compact separable unimodular groups for the range of indices $1<p\leq 2 \leq q<\infty$. Our approach is based on the operator algebras techniques. The…

We find optimal conditions on $m$-linear Fourier multipliers to give rise to bounded operators from a product of Hardy spaces $H^{p_j}$, $0<p_j\le 1$, to Lebesgue spaces $L^p$. The conditions we obtain are necessary and sufficient for…

Let G be a locally compact group L^p(G) be the usual L^p-space for 1 =< p =< infty and A(G) be the Fourier algebra of G. Our goal is to study, in a new abstract context, the completely bounded multipliers of A(G), which we denote…

In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure

We study the action of Fourier Integral Operators (FIOs) of H{\"o}rmander's type on ${\mathcal{F}} L^p({\mathbb {R}}^d_{comp}$, $1\leq p\leq\infty$. We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be…

Consider a non-doubling manifold with ends $M = \mathfrak{R}^{n}\sharp\, {\mathbb R}^{m}$ where $\mathfrak{R}^n=\mathbb{R}^n\times \mathbb{S}^{m-n}$ for $m> n \ge 3$. We say that an operator $L$ has a generalised Poisson kernel if $\sqrt{…

We consider quasiradial Fourier multipliers, i.e. multipliers of the form $m(a(\xi))$ for a class of distance functions $a$. We give a necessary and sufficient condition for the multiplier transformations to be bounded on $L^p$ for a…

Let $T$ be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of $\mathbb R^n$. We assume that the associated kernel of $T$ satisfies some mild regularity condition which is weaker than the usual…

We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish H\"ormander-type $L^{p}-L^{q}$ boundedness results for the range $1<p\leq 2\leq q<\infty$. The analysis…

In this paper we study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that H\"ormander type conditions on the Fourier multipliers imply $L^p$-boundedness. We express these conditions…

We provide a characterization of $\mathrm{BMO}$ in terms of endpoint boundedness of commutators of singular integrals. In particular, in one dimension, we show that $\|b\|_{\mathrm{BMO}}\eqsim B$, where $B$ is the best constant in the…

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…

In this paper, we prove that the oscillation operator, variation operator and maximal differential transform associated with the approximate identities are bounded from ${\rm BMO}({\mathbb R}^n)$ to its subspace ${\rm BLO}({\mathbb R}^n)$.

Let L be a generator of a semigroup satisfying the Gaussian upper bounds. In this paper, we study further a new BMO_L space associated with L which was introduced recently by Duong and Yan. We discuss applications of the new BMO_L spaces in…

In this paper we have studied Fourier multipliers and Littlewood-Paley square functions in the context of modulation spaces. We have also proved that any bounded linear operator from modulation space $\mathcal{M}_{p,q}(\R^n), 1\leq p,q\leq…

In this article we extend recent results by the first author on the necessity of $BMO$ for the boundedness of commutators on the classical Lebesgue spaces. We generalize these results to a large class of Banach function spaces. We show that…

In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-H\"ormander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves…

Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.

We prove the global $L^p$-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical H\"ormander classes $S^{m}_{\rho, \delta}(\mathbb{R}^n)$ for…