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Weighted weak (1,1) and weighted $$L^ p$$ estimates for oscillating kernels. (English) Zbl 0594.42007
Summary: Weak type (1,1) and strong type (p,p) inequalities are proved for operators defined by oscillating kernels. The techniques are sufficiently general to derive versions of these inequalities using weighted norms.

##### MSC:
 42A50 Conjugate functions, conjugate series, singular integrals 42A45 Multipliers in one variable harmonic analysis 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
##### Keywords:
oscillating kernels; inequalities; weighted norms
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