Hardy-type inequalities, Weighted Fourier inequalities, Weighted Hardy Spaces. Integration is the unifying concept of Analysis.
Estimates are comparisons between integrals, our method of relating one to another.
Where integrals represent measurable quantities, estimates give us new truths about what we have measured. Estimates also give us information about quantities we can not measure directly. My work is in Harmonic Analysis. The Fourier Transform converts information about the amplitude of a wave to information about its frequency. They are based on new, very sensitive techniques that take into account both the amplitude and frequency.