Related papers: On multilinear determinant functionals

We prove uniform $L^p$ bounds for multilinear operators which are given by multipliers whose symbols are singular on a one dimensional subspace. The novelty is that these bounds are uniform in the choice of the subspace.

We characterize the $L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions.

We prove $L^p$ estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimates for the general bi-parameter form of the twisted…

A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace…

Bourgain in his seminal paper [2] about the analysis of maximal functions associated to convex bodies, has estimated in a sharp way the $L^2$-operator norm of the maximal function associated to a kernel $K\in L^1,$ with differentiable…

We establish global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on product of $L^p$ spaces by proving endpoint boundedness on suitable products spaces containing combinations of the…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

In this work, we establish $L^{p_1}\times \cdots\times L^{p_m}\to L^p$ bounds for maximal multi-(sub)linear singular integrals associated with homogeneous kernels $\frac{\Omega(\vec{\boldsymbol{y}}')}{|\vec{\boldsymbol{y}}|^{mn}}$ where…

Let $\sigma=(\sigma_{1},\sigma_{2},\dots,\sigma_{n})\in \mathbb{S}^{n-1}$ and $d\sigma$ denote the normalised Lebesgue measure on $\mathbb{S}^{n-1},~n\geq 2$. For functions $f_1, f_2,\dots,f_n$ defined on $\R$ consider the multilinear…

Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…

We study the $L^p$ boundedness and find the norm of a class of integral operators induced by the reproducing kernel of Fock spaces over $C^n$.

We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving…

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. The alpha-harmonic functions and their first-order partial derivative functions on unit disk are estimated…

We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the operators are smooth or rough in the spatial variables. The results are obtained by…

This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to $L^p$-improving inequalities for Radon-like transforms over polynomial submanifolds of intermediate…

In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…

We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The…

Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional…

We study a new class of Fourier integral operators defined in R^N. Their symbols are allowed to satisfy a differential inequality with certain multi-parameter characteristic. We prove these operators of order -(N-1)/2 bounded from the…