Related papers: Pointwise multipliers on martingale Campanato spac…

Let $G$ be $PGL(n,F)$, $n \geq 3$, $F$ a certain non-archimedean local field; or let $G$ be $PSL(2,\mathbb{R}) \times \cdots \times PSL(2,\mathbb{R})$. Let $\Gamma$ be a lattice in $G$, and let $( \Lambda_n )$ be a sequence of lattices in…

In this paper, we introduce Hardy spaces with variable exponents defined on a probability space and develop the martingale theory of variable Hardy spaces. We prove the weak type and strong type inequalities on Doob's maximal operator and…

We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, CMO, local Morrey-type spaces, etc., and investigate the interpolation property of $B_w^u$-function spaces. We also apply it to the boundedness…

We show that a continuous bilinear mapping P: C(I) \times C(I) \to C(I) can be presented in the form P(f,g) = B((Af)(Ag)), where A and B are bounded linear operators on C(I) and multiplication is defined pointwise, if and only if for all t…

Let $\mathcal{M}(n,m;\F \bp^n)$ be the configuration space of $m$-tuples of pairwise distinct points in $\F \bp^n$, that is, the quotient of the set of $m$-tuples of pairwise distinct points in $\F \bp^n$ with respect to the diagonal action…

Using the fractional derivative, considered in the Caputo sense, we study an analytical technique associated with the variational iteration method for the fractional generalized $\alpha$-time Burgers' equation with $\alpha>0$ and obtain…

We consider a class of spectral multipliers on stratified Lie groups which generalise the class of H\"ormander multipliers and include multipliers with an oscillatory factor. Oscillating multipliers have been examined extensively in the…

For a Hilbert space H included in L^1_{loc} (R) of functions on $R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L^2(R) as well as our…

We study $l$-very ample, ample and semi-ample divisors on the blown-up projective space $\mathbb{P}^n$ in a collection of points in general position. We establish Fujita's conjectures for all ample divisors with the number of points bounded…

Let $L$ be a convex cone of real random variables on the probability space $(\Omega,\mathcal{A},P_0)$. The existence of a probability $P$ on $\mathcal{A}$ such that $$ P \sim P_0,\quad E_P \abs{X}< \infty\, \text{ and } \, E_P(X) \leq 0\,…

In this paper, the main aim is to consider the boundedness of the fractional maximal commutator $M_{\alpha,b}$ and the nonlinear commutator $[b, M_{\alpha}]$ on the Lebesgue spaces over some stratified Lie group $\mathbb{G}$ when $b$…

We study some basic properties of generalized Morrey spaces $\mathcal{M}^{p,\phi}(\R^{d})$. Also, the problem $-\mbox{div}(|\nabla u|^{p-2}\nabla u)+V|u|^{p-2}u=0$ in $\Omega$, where $\Omega$ is a bounded open set in $\R^d$, and potential…

We characterize one-sided weighted Sobolev spaces $W^{1,p}(\mathbb{R},\omega)$, where $\omega$ is a one-sided Sawyer weight, in terms of a.e.~and weighted $L^p$ limits as $\alpha\to1^-$ of Marchaud fractional derivatives of order $\alpha$.…

We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on square matrices, which we refer to as the recombinant, agrees…

The main purpose of this paper is to give an estimate for the Fourier Laguerre transform on Hardy spaces in the setting of Laguerre hypergroup. The atomic and molecular characterization is investigated which allows us to prove a version of…

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…

We develop a special multilinear complex interpolation theorem that allows us to prove an optimal version of the bilinear H\"ormander multiplier theorem concerning symbols that lie in the Sobolev space $L^r_s(\mathbb R^{2n})$, $2\le…

In this paper, the authors prove the boundedness of commutators generated by the weighted Hardy operator on weighted $\lambda$-central Morrey space with the weight $\omega$ satisfying the doubling condition. Moreover, the authors give the…

Following Sarason's classification of the densely defined multiplication operators over the Hardy space, we classify the densely defined multipliers over the Sobolev space, $W^{1,2}[0,1]$. In this paper we find that the collection of such…

We consider a tuple $\Phi = (\phi_1,\ldots,\phi_m)$ of commuting maps on a finitary matroid $X$. We show that if $\Phi$ satisfies certain conditions, then for any finite set $A\subseteq X$, the rank of $\{\phi_1^{r_1}\cdots\phi_m^{r_m}(a):a…