Related papers: Singular Integral Operators on Variable Lebesgue S…

We study a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local variant to be bounded on…

We prove $L^p$ bounds for the extensions of standard multilinear Calder\'on-Zygmund operators to tuples of UMD spaces tied by a natural product structure. This can, for instance, mean the pointwise product in UMD function lattices, or the…

We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…

Many concepts of Fourier analysis on Euclidean spaces rely on the specification of a frequency point. For example classical Littlewood Paley theory decomposes the spectrum of functions into annuli centered at the origin. In the presence of…

This article consists of two connected parts. In the first part, we study the shift invariant subspaces in certain $\mathcal{P}^2(\mu)$-spaces, which are the closures of analytic polynomials in the Lebesgue spaces $\mathcal{L}^2(\mu)$…

While the local $L^p$-boundedness of nondegeneral Fourier integral operators is known from the work of Seeger, Sogge and Stein, not so many results are available for the global boundedness on $L^p(\mathbb R^n)$. In this paper we give a…

We consider the following model of degenerate and singular oscillatory integral operators: \begin{equation*} Tf(x)=\int_{\mathbb{R}} e^{i\lambda S(x,y)}K(x,y)\psi(x,y)f(y)dy, \end{equation*} where the phase functions are homogeneous…

We prove $L^p_{comp}\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities…

In the present paper, we consider elliptic operators $L=-\textrm{div}(A\nabla)$ in a domain bounded by a chord-arc surface $\Gamma$ with small enough constant, and whose coefficients $A$ satisfy a weak form of the Dahlberg-Kenig-Pipher…

We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf…

Let $\Gamma$ be a graph equipped with a Markov operator $P$. We introduce discrete fractional Littlewood-Paley square functionals and prove their $L^p$-boundedness under various geometric assumptions on $\Gamma$.

In this paper we investigate the mapping properties of periodic Fourier integral operators in $L^p(\mathbb{T}^n)$-spaces. The operators considered are associated to periodic symbols (with limited regularity) in the sense of Ruzhansky and…

The $L^p$-spaces, with $p \not = \infty$, form a partial algebra $(L^p(\Omega), \Gamma, \cdot)$ with pointwise multiplication of functions. The Sobolev spaces $W^{k,p}(\Omega)$, delineated by weak derivatives as subspaces of $L^p$-spaces is…

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…

In this paper, we establish sufficient conditions for a singular integral $T$ to be bounded from certain Hardy spaces $H^p_L$ to Lebesgue spaces $L^p$, $0< p \le 1$, and for the commutator of $T$ and a BMO function to be weak-type bounded…

We define and study homogeneous kinetic Sobolev spaces adapted to the Kolmogorov equation. We consider both local and non-local diffusion. The spaces are built from the Lebesgue spaces L p for all integrability exponents p $\in$ (1,…

In this paper, we first introduce $L^{\sigma_1}$-$(\log L)^{\sigma_2}$ conditions satisfied by the variable kernels $\Omega(x,z)$ for $0\leq\sigma_1\leq1$ and $\sigma_2\geq0$. Under these new smoothness conditions, we will prove the…

The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the $L^2(\mu)$-boundedness of certain singular integral operators to the geometric properties of the support of measure $\mu$, e.g.…

We show that the Hardy-Littlewood maximal operator and a class of Calder\'on-Zygmund singular integrals satisfy the strong type modular inequality in variable $L^p$ spaces if and only if the variable exponent $p(x)\sim const$.

Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which…