Related papers: Sparse domination for rough multilinear singular i…

Let T_t=e^{-tL} be a semigroup of self-adjoint linear operators acting on L^2(X,mu), where (X,d mu) is a space of homogeneous type. We assume that T_t has an integral kernel T_t(x,y) which satisfies the upper and lower Gaussian bounds:…

We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation theorems we first revisit a result of Figiel concerning the…

We study truncated bilinear forms associated with synchronized kernels \[ K(x,y)=k(\phi(x),\psi(y)), \] where the singularity is governed by a one-dimensional kernel $k$, while the geometry is encoded by the phases $\phi$ and $\psi$. The…

In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ in terms of first-order differences in a uniform domain $\Omega$. The characterization is valid for any positive, non-integer real…

In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular…

In this paper we study Coifman type estimates and weighted norm inequalities for singular integral operators $T$ and its commutators, given by the convolution with a vector valued kernel $K$. We define a weaker H\"ormander type condition…

Nous poursuivons l'\'etude d'un contr\^ole \'epars d'un op\'erateur singulier. Plus pr\'ecis\'ement nous expliquons comment on peut conserver certaines propri\'et\'es de l'op\'erateur initial \`a travers un tel contr\^ole et d\'ecrivons…

Let $M$ be a smooth manifold of dimension $2n$, and let $O_{M}$ be the dense open subbundle in $\wedge^{2}T^{\ast}M$ of $2$-covectors of maximal rank. The algebra of $\operatorname*{Diff}M$-invariant smooth functions of first order on…

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…

We prove that in any metric space $(X,d)$ the singular integral operators {equation*} T^k_{\mu,\ve}(f)(x)=\int_{X\setminus B(x,\varepsilon)}k(x,y)f(y)d\mu (y).{equation*} converge weakly in some dense subspaces of $L^2(\mu)$ under minimal…

We consider Volterra-type integration operators $T_g$ between Bergman spaces induced by weights $\omega$ satisfying a doubling property. We derive estimates for the operator norms, essential and weak essential norms of $T_g: A_\omega^p \to…

Let $v,~\omega_1, ~\omega_2$ be weights and $1<p_1, ~p_2<\infty.$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $(\omega_1, \omega_2)\in RH(p_1, p_2).$ For the multisublinear maximal operator $\mathfrak{M}$ in martingale…

We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in \cite{CS}. Since the order of differentiability of…

The aim of this paper is to obtain mixed weak-type inequalities for multilinear fractional operators, extending results by F. Berra, M. Carena and G. Pradolini \cite{BCP}. We prove that, under certain conditions on the weights, there exists…

We study the minimizing problem $\inf\left\{\displaystyle\int_{\Omega}p(x)|\nabla u|^{2}dx,\,u\in H^{1}_{0}(\Omega),\,\|u\|_{L^{\frac{2N}{N-2}}(\Omega)}=1\right\}$ where $\Omega$ is a smooth bounded domain of $\R^{N}$, $N\geq 3$ and $p$ a…

In this paper, the multilinear fractional strong maximal operator $\mathcal{M}_{\mathcal{R},\alpha}$ associated with rectangles and corresponding multiple weights $A_{(\vec{p},q),\mathcal{R}}$ are introduced. Under the dyadic reverse…

Let $\Omega$ be a bounded open interval, let $p>1$ and $\gamma>0$, and let $m:\Omega\rightarrow\mathbb{R}$ be a function that may change sign in $\Omega $. In this article we study the existence and nonexistence of positive solutions for…

Convolution type Calder\'on-Zygmund singular integral operators with rough kernels $\pv \Om(x)/|x|^n$ are studied. A condition on $\Om$ implying that the corresponding singular integrals and maximal singular integrals map $L^p \to L^p$ for…

In this paper, we will study the boundedness properties of multilinear Calderon--Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains $\Omega$, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term $H$, in term of the size of $\Omega$,…