Sharp $L^p-L^q$ estimates for a class of averaging operators

Alex Iosevich; Eric Sawyer

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.

$L^{p}$ and Hölder estimates for pseudodifferential operators : sufficient conditions

Richard Beals (1979)

Annales de l'institut Fourier

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Continuity in $L^{p}$ spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.

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 $C \subset (T^{*} X ∖ 0) \times (T^{*} Y ∖ 0)$ . These canonical relations, which arise naturally in integral geometry, are such that $π$ : $C \to T^{*} Y$ is a Whitney fold and $ρ$ : $C \to T^{*} X$ is a blow-down mapping. If $A \in I^{m} (C)$ , $B \in I^{m^{'}} (C^{t})$ , then $B A \in I^{m + m^{'}, 0} (Δ, Λ)$ 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 ∈ L_loc ^r(R^d), then the differential inequality |Δu| ≤ V |∇u| has the strong unique continuation property in the following sense: If u belongs to the Sobolev space W_loc ^2,p and if |Δu|...

Interior curvature estimates for hypersurfaces of prescribed mean curvature

Klaus Ecker, Gerhard Huisken (1989)

Annales de l'I.H.P. Analyse non linéaire

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

L estimates for degenerate elliptic equations.

L p and Hölder estimates for pseudodifferential operators : sufficient conditions

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

On oscillatory integral operators with folding canonical relations

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

Interior curvature estimates for hypersurfaces of prescribed mean curvature

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

$L^{p}$ and Hölder estimates for pseudodifferential operators : sufficient conditions

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