相关论文: $L_p$-Theory of Type $1,1$-Operators
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove…
We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…
In this paper we study some problems related with the theory of multidimensional $p$-adic wavelets in connection with the theory of multidimensional $p$-adic pseudo-differential operators (in the $p$-adic Lizorkin space). We introduce a new…
We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable…
We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\mathbb R}^d;{\mathbb R}^m)$, $(d,m \ge 1)$ with $p\in [1,+\infty)$. Sufficient conditions for the associated evolution operator ${\bf…
Let $s\ge 1$, $\omega ,\omega_0\in \mathscr P_{E,s}^0$, $a\in \Gamma _{s}^{(\omega_0)}$, and let $\mathscr B$ be a suitable invariant quasi-Banach function space, Then we prove that the pseudo-differential operator $\operatorname{Op} (a)$…
For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction…
In this paper we consider unbounded weighted conditional type operators on the space Lp, we give some conditions under which they are densely defined and we obtain a dense subset of the domain. Also, we get that a WCT operator is continuous…
A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…
The continouity and compactness of embedding operators in in Sobolev-Lions type spaces are derived. By applying this result separability properties of degenerate anisotropic differential operator equations, well-posedeness and Strichartz…
We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The…
In this work we consider the following $\alpha$-stable-like operator (a class of pseudo-differential operator) $$ {\mathscr L} f(x):=\int_{\mathbb R^d}[f(x+\sigma_x y)-f(x)-1_{\alpha\in[1,2)}1_{|y|\leq 1}\sigma_x y\cdot\nabla f(x)]\nu_x(d…
We establish the following results on higher order $\mathcal{S}^p$-differentiability, $1<p<\infty$, of the operator function arising from a continuous scalar function $f$ and self-adjoint operators defined on a fixed separable Hilbert…
In this paper, we study the boundedness of pseudo-differential operators with symbols in $S_{\rho,\delta}^m$ on the modulation spaces $M^{p,q}$. We discuss the order $m$ for the boundedness $\mathrm{Op}(S_{\rho,\delta}^m) \subset…
Recently, Bansah and Sehba studied in [3] the boundedness of a family of Hilbert-type integral operators, where they characterized the $L^{p}-L^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. In this paper, we deal with…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
This paper is devoted to the study of operator-valued Triebel-Lizorkin spaces. We develop some Fourier multiplier theorems for square functions as our main tool, and then study the operator-valued Triebel-Lizorkin spaces on $\mathbb{R}^d$.…
We recover for discrete Schr\"odinger operators on the lattice Z, stronger analogues of the results by Weder, Galtabiar and Yajima and by D'Ancona and Fanelli on R.
We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree <3, we prove…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…