Logarithmic Bounds for Oscillatory Singular Integrals on Hardy Spaces
نویسندگان
چکیده
منابع مشابه
Bounds of Singular Integrals on Weighted Hardy Spaces and Discrete Littlewood–Paley Analysis
We apply the discrete version of Calderón’s reproducing formula and Littlewood–Paley theory with weights to establish the H w → H w (0 < p < ∞) and H w → Lw (0 < p ≤ 1) boundedness for singular integral operators and derive some explicit bounds for the operator norms of singular integrals acting on these weighted Hardy spaces when we only assume w ∈ A∞. The bounds will be expressed in terms of ...
متن کاملBoundedness of Oscillatory Singular Integrals on Weighted Sobolev Spaces
In this paper, an oscillatory singular integral operator T deened by T f (x) = Z IR e ixP(y) f (x ? y) y dy is showed to be bounded on a weighted Sobolev space H
متن کاملSparse 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.
متن کاملBoundedness of Singular Integrals in Weighted Anisotropic Product Hardy Spaces
Let Ai for i = 1, 2 be an expansive dilation, respectively, on R n and R and ~ A ≡ (A1, A2). Denote by A∞(R × R; ~ A) the class of Muckenhoupt weights associated with ~ A. The authors introduce a class of anisotropic singular integrals on R×R, whose kernels are adapted to ~ A in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors est...
متن کاملOn Multilinear Oscillatory Integrals, Nonsingular and Singular
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Function Spaces
سال: 2016
ISSN: 2314-8896,2314-8888
DOI: 10.1155/2016/1570109