Philip T. Gressman

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math.CA2008

Rank and regularity for averages over submanifolds

Philip T. Gressman

This paper establishes endpoint $L^{p} - L^{q}$ and Sobolev mapping properties of Radon-like operators which satisfy a homogeneity condition (similar to semiquasihomogeneity) and a condi…

math.CA2007

Uniform estimates for cubic oscillatory integrals

Philip T. Gressman

This paper establishes the optimal decay rate for scalar oscillatory integrals in $n$ variables which satisfy a nondegeneracy condition on the third derivatives. The estimates prov…