Related papers: Fractional integration with singularity on the lig…
In this paper, we study the boundedness theory for maximal Calder\'on-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calder\'on-Zygmund…
We prove the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra…
In this paper we introduce a new family of topological convolution algebras of the form $\bigcup_{p\in\mathbb N} L_2(S,\mu_p)$, where $S$ is a Borel semi-group in a locally compact group $G$, which carries an inequality of the type…
We prove the cone theorem for varieties with LCIQ singularities using deformation theory of stable maps into Deligne-Mumford stacks. We also obtain a sharper bound on $-(K_X+D)$-degree of $(K_X+D)$-negative extremal rays for projective…
In this paper we have characterized the space of summability kernels for the case p=1 and p=2. For other values of p we give a necessary condition for a function $\Lambda$ to be a summability kernel. For the case p=1, we have studied the…
We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This…
In this paper we define an integral operator on Lp and obtain its degree of convergence in the appropriate norm. By specializing the kernel of the integral operator we obtain many known results as corollaries. We have also applied our…
We study the inequalities of the type $|\int_{\mathbb{R}^d} \Phi(K*f)| \lesssim \|f\|_{L_1(\mathbb{R}^d)}^p$, where the kernel $K$ is homogeneous of order $\alpha - d$ and possibly vector-valued, the function $\Phi$ is positively…
Light-cone quantization always involves the solution of differential constraint equations. The solutions to these equations include integration constants (fields independent of $x_-$). These fields are unphysical but when they are…
Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…
We investigate possible quantifications of strictly singular operators, $l_{p}$-strictly singular operators, $c_{0}$-strictly singular operators, strictly cosingular operators, $l_{p}$-strictly cosingular operators. We prove quantitative,…
The optimal sufficient conditions for the $L^p$-to-$L^q$ compactness of commutators of singular integral operators of both Calder\'on-Zygmund and of rough type are shown in the different exponent ranges $``q>p"$, $``q=p"$ and $``q<p"$ to…
We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…
QCD in non-integer $d=4-2\epsilon$ space-time dimensions enjoys conformal invariance at the special fine-tuned value of the coupling. Counterterms for composite operators in minimal subtraction schemes do not depend on $\epsilon$ by…
We prove that the flag kernel singular integral operators of Nagel-Ricci-Stein on a homogeneous group are bounded on the Lp spaces. The gradation associated with the kernels is the natural gradation of the underlying Lie algebra. Our main…
We study the structure of strictly singular non-compact operators between $L_p$ spaces. Answering a question raised in [Adv. Math. 316 (2017), 667-690], it is shown that there exist operators $T$, for which the set of points…
We consider the algebra of mixed multidimensional integral operators. In particular, Fredholm integral operators of the first and second kind belongs to this algebra. For the piecewise constant kernels we provide an explicit representation…
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 introduce probability-preserving convolution algebras on cones of positive semidefinite matrices over one of the division algebras $\b F = \b R, \b C$ or $\b H$ which interpolate the convolution algebras of radial bounded…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…