Related papers: $H^1$ to $L^q$-boundedness of fractional integral …

We study the Hp-Lq boundedness of certain integral operators of fractional type.

We study the boundedness of certain fractional integral operators from Hp(.) into Lq(.). We also obtain the Hp(.)- Hq(.) boundedness of the Riesz potential.

In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…

In this paper, we study a class of multilinear fractional integral operators which have correlation kernels $\prod_{1\leq i<j \leq k}|x_i-x_j|^{-\alpha_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators…

In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable…

We study a family of convolution operators whose kernels have a singularity on the unit sphere. As a result, we prove the regarding L^p-L^q Sobolev inequalities.

We study a family of fractional integral operators defined in $\mathbb{R}^3$ whose kernels are distributions associated with Zygmund dilations: $(x_1, x_2, x_3) \rightarrow (\delta_1 x_1, \delta_2 x_2, \delta_1\delta_2 x_3)$ for…

Let $\mathcal K$ be a flag kernel on a homogeneous nilpotent Lie group $G$. We prove that operators $T$ of the form $T(f)= f*\mathcal K$ form an algebra under composition, and that such operators are bounded on $L^{p}(G)$ for $1<p<\infty$.

In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…

We study a family of strong fractional integral operators whose kernels have singularity on every coordinate subspace. We prove a two-weight $L^p$-$L^q$-norm inequality by allowing only one of the weights to satisfy $A_p\times…

In this article we consider the classical singular integral operator over a local field with rough kernels. We study the boundedness of such an operator on different function spaces by relaxing the smoothness condition on kernels.

In this paper, we study a family of fractional integral operators whose kernel carrying a critical index has singularity on the light-cone in R^n+1.

In the paper, we consider integral operators with non-negative kernels satisfying conditions, which are less restrictive than conditions studied earlier. We establish criteria for the boundedness of these operators in Lebesgue spaces.

We investigate certain singular integral operators with Riesz-type kernels on s-dimensional Ahlfors-David regular subsets of Heisenberg groups. We show that $L^2$-boundedness, and even a little less, implies that $s$ must be an integer and…

Flag kernels are tempered distributions which generalize these of Calderon-Zygmund type. For any homogeneous group $\mathbb{G}$ the class of operators which acts on $L^{2}(\mathbb{G})$ by convolution with a flag kernel is closed under…

For a wide family of multivariate Hausdorff operators, a new stronger condition for the boundedness of an operator from this family on the real Hardy space $H^1$ by means of atomic decomposition.

In this paper, we give an atomic decomposition characterization of flag Hardy spaces $H^p_F({\rr}^n\times {\rr}^m)$ for $0<p\le 1$, which were introduced in \cite{hl1}. A remarkable feature of atoms of such flag Hardy spaces is that these…

We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…

We investigate a class of Fourier integral operators with weakened symbols, which satisfy a multi-parameter differential inequality in $\R^n$. We establish that these operators retain the classical $L^p$ boundedness and the $H^1$ to $L^1$…

In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential operators with possibly singular kernels. More precisely, in…