Here is established the global existence of smooth solutions to a generalized nonlinear equation of Schrödinger type in the usual Sobolev spaces H and certain weighted Sobolev spaces by using Leray-Schauder fixed point theorem and delicate a priori estimates.

Abstract In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces L p (ℝ n ), Hardy H ) general mixed norm spaces, which implies almost everywhere convergence of such operator. this paper, we study rate some sobolev type spaces.

Abstract. Let u(x, t) be the solution to the free time-dependent Schrödinger equation at the point (x, t) in space-time Rn+1 with initial data f . We characterize the size of u in terms Lp(Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Ḣs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interp...

Let u(x; t) be the solution to the free time-dependent Schrr odinger equation at the point (x; t) in space-time R n+1 with initial data f. We characterize the size of u in terms L p (L q)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces _ H s (R n). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interpo...

Abstract In this paper, bilinear pseudo‐differential operators with symbols in the Hörmander class are considered. particular, boundedness of these on Sobolev spaces is established. Our main result proved by using symbolic calculus and those certain S 0, 0 ‐type Lebesgue spaces.

In this paper, the authors establish the sharp maximal estimates for the multilinear iterated commutators generated by [Formula: see text] functions and multilinear singular integral operators with generalized kernels. As applications, the boundedness of this kind of multilinear iterated commutators on the product of weighted Lebesgue spaces and the product of variable exponent Lebesgue spaces ...

Let D be a bounded domain in C with C boundary. Many holomorphic function spaces over D have been introduced in last half century, such as Hardy, Bergman, Besov and Sobolev spaces. Properties (boundary behaviour ect.) of functions in those function spaces have been received a great deal of studies. Readers can see parts of them from the following books [26] [29], [66], [71], [75], [76] and refe...

In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady nonlinear Leray–Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes. This is achieved by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes ...

We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajtasz Sobolev spaces, weighted Sobolev spaces, Upper-gradients, etc). We then introduce the notion of variational p-capacity and discuss its relation with the geometric properties of the metric space. The notions of p-parabolic ...