Let H be Monge-Ampère singular integral operator, [Formula: see text], and [Formula: see text]. It is proved that the commutator [Formula: see text] is bounded from [Formula: see text] to [Formula: see text] for [Formula: see text] and from [Formula: see text] to [Formula: see text] for [Formula: see text]. For the extreme case [Formula: see text], a weak estimate is given.

For quasilinear integro-diierential equations of the form u t ?aA(u) = f, where a is a scalar singular integral kernel that behaves like t ? , 1 2 < 1 and A is a second order quasilinear elliptic operator in divergence form, solutions are found for which A(u) is integrable over space and time.

A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT ∗C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ |T |, where J is an auxiliary conjugation commuting with |T | = √ T ∗T . We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compr...

in this paper, we study the convexity of the integral operator

Any compact C∞ manifold with boundary admits a Riemann metric on its interior taking the form x−4dx2 + x−2h′ near the boundary, where x is a boundary defining function and h′ is a smooth symmetric 2-cotensor restricting to be positive-definite, and hence a metric, h, on the boundary. The scattering theory associated to the Laplacian for such a ‘scattering metric’ was discussed by the first auth...