Hardy Spaces on the Plane and Double Fourier Transforms.
Hausdorff dimension, projections, and the Fourier transform.
This is a survey on transformation of fractal type sets and measures under orthogonal projections and more general mappings.
Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville operator.
Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.
We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...
Hyperbolic singular integral operators.
We define a class of integral operators which are singular relative to the hyperbolic metric in simply connected domains of the plane. We study the necessary and sufficient conditions for such operators to be bounded on L2 of the upper half plane relative to the hyperbolic metric.