Displaying similar documents to “Sharp L p - L q estimates for a class of averaging operators”

L estimates for degenerate elliptic equations.

Antonio Sánchez-Calle (1988)

Revista Matemática Iberoamericana

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In this note we are going to address the question of when a second order differential operator is controlled by a subelliptic second order differential operator.

Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

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We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ⊂ ( T * X ∖ 0 ) × ( T * Y ∖ 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C → T * Y is a Whitney fold and ρ : C → T * X is a blow-down mapping. If A ∈ I m ( C ) , B ∈ I m ' ( C t ) , then B A ∈ I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

On oscillatory integral operators with folding canonical relations

Allan Greenleaf, Andreas Seeger (1999)

Studia Mathematica

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Sharp L p estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation C Φ projects to T*X and T*Y with fold singularities.

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

Thomas H. Wolff (1990)

Revista Matemática Iberoamericana

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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|...