Related papers: Bilinear estimates on Morrey spaces by using avera…
In this paper, we consider the boundedness of fractional type multilinear commutators generated by fractional integral with rough variable kernel and local Campanato functions on both generalized local (central) Morrey spaces and…
Let $T$ be a Fourier integral operator of order $-(n-1)/2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of…
In this paper, we establish a new improved Sobolev inequality based on a weighted Morrey space. To be precise, there exists $C=C(n,m,s,\alpha)>0$ such that for any $u,v \in {\dot{H}}^s(\mathbb{R}^{n})$ and for any $\theta \in…
In this note, we consider a Fourier integral operator defined by \begin{align*} T_{\phi,a}f(x) = \int_{\mathbb{R}^{n}}e^{i\phi(x,\xi)}a(x,\xi)\widehat{f} \xi)d\xi, \end{align*}here $a$ is the amplitude, and $\phi$ is the phase. Let…
The purpose of this paper is to establish some neccessary and sufficient conditions for the boundedness of a general class of multilinear Hausdorff operators that acts on the product of some two weighted function spaces such as the two…
Let $0<t<\infty$, $0<\alpha<n$, $1<p<r<\infty$ and $1<q<s<\infty$. In this paper, we prove that $b\in B M O\left(\mathbb{R}^{n}\right)$ if and only if the commutator $[b, T_{\Omega,\alpha}]$ generated by the fractional integral operator…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and…
We prove fractional Leibniz rules and related commutator estimates in the settings of weighted and variable Lebesgue spaces. Our main tools are uniform weighted estimates for sequences of square-function-type operators and a bilinear…
In this paper, we establish BMO estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, respectively.
In this paper, some boundedness for commutators of fractional integrals are obtained on Herz-Morrey spaces with variable exponent applying some properties of varible exponent and $\BMO$ function.
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…
In this note we give a criterion for the existence of a fractional-linear integral for a geodesic flow on a Riemannian surface and explain that modulo M\"obius transformations the moduli space of such local integrals (if nonempty) is either…
We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The…
We show that a continuous bilinear mapping P: C(I) \times C(I) \to C(I) can be presented in the form P(f,g) = B((Af)(Ag)), where A and B are bounded linear operators on C(I) and multiplication is defined pointwise, if and only if for all t…
We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…
We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain…
We consider some bilinear Fourier multiplier operators and give a bilinear version of Seeger, Sogge, and Stein's result for Fourier integral operators. Our results improve, for the case of Fourier multiplier operators, Rodr\'iguez-L\'opez,…
In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order $\alpha > 0$ in Bochner-Lebesgue spaces. We specifically address the remaining cases concerning its boundedness when $\alpha > 1/p$.…