Bounds for oscillatory integrals and L²-theory of the corresponding singular integrals
نویسندگان
چکیده
منابع مشابه
Sparse bounds for oscillatory and random singular integrals
Let TP f(x) = ∫ e K(y)f(x − y) dy, where K(y) is a smooth Calderón–Zygmund kernel on R, and P be a polynomial. We show that there is a sparse bound for the bilinear form 〈TP f, g〉. This in turn easily implies Ap inequalities. The method of proof is applied in a random discrete setting, yielding the first weighted inequalities for operators defined on sparse sets of integers.
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Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L norm inequalities are established for multilinear integral operators of Calderón-Zygmund type which incorporate oscillatory factors e iP , where P is a real-valued polynomial. A related problem concerning upper bounds for measures of sublevel sets is solved.
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1984
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-79-1-35-50