Displaying similar documents to “The non-existence of L p -estimates for certain translation-invariant operators”

Some multiplier theorems on the sphere.

R. O. Gandulfo, G. Gigante (2000)

Collectanea Mathematica

Similarity:

The n-dimensional sphere, E, can be seen as the quotient between the group of rotations of R n+1 and the subgroup of all the rotations that fix one point. Using representation theory, one can see that any operator on Lp (Sigma n) that commutes with the action of the group of rotations (called multiplier) may be associated with a sequence of complex numbers. We prove that, if a certain discrete derivative of a given sequence represents a bounded multiplier on LP (E 1), then the given...

Unique continuation for |Δu| ≤ V |∇u| and related problems.

Thomas H. Wolff (1990)

Revista Matemática Iberoamericana

Similarity:

Much of this paper will be concerned with the proof of the following Theorem 1. Suppose d ≥ 3, r = max {d, (3d - 4)/2}. If V ∈ Lloc r(Rd), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space Wloc 2,p and if |Δu|...

L-estimates for the wave equation on the Heisenberg group.

Detlef Müller, Elias M. Stein (1999)

Revista Matemática Iberoamericana

Similarity:

Let £ denote the sub-Laplacian on the Heisenberg group H. We prove that e / (1 - £) extends to a bounded operator on L(H), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.

Multipliers for Hermite expansions.

Sundaram Thangavelu (1987)

Revista Matemática Iberoamericana

Similarity:

The aim of this paper is to prove certain multiplier theorems for the Hermite series.