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Weighted norm inequalities for the continuous square functions. (English) Zbl 0689.42016

Summary: We prove new weighted norm inequalities for real-variable analogues of the Lusin area function. We apply our results to obtain new: (i) weighted norm inequalities for singular integral operators: (ii) weighted Sobolev inequalities: (iii) eigenvalue estimates for degenerate Schrödinger operators.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
42B15 Multipliers for harmonic analysis in several variables
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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