Discrete analogues of singular Radon transforms
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Publication:5749788
DOI10.1090/S0273-0979-1990-15973-7zbMath0718.42015MaRDI QIDQ5749788
Publication date: 1990
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
BMOCalderón-Zygmund convolution kernelBourgain's maximal ergodic theoremdiscrete singular Radon transform
Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Estimates on character sums (11L40)
Related Items (23)
Oscillation and variation for singular integrals in higher dimensions ⋮ On a discrete bilinear singular operator ⋮ Discrete Radon transforms and applications to ergodic theory ⋮ The Hardy-Littlewood maximal operator on discrete Morrey spaces ⋮ Calderón-Zygmund operators on amalgam spaces and in the discrete case ⋮ A discrete Carleson theorem along the primes with a restricted supremum ⋮ Dixmier traces for discrete pseudo-differential operators ⋮ Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: \(\ell^p\) bounds for \(p > 1\) ⋮ Sparse Bounds for Random Discrete Carleson Theorems ⋮ Sparse bounds for the discrete cubic Hilbert transform ⋮ Maximal operators associated to discrete subgroups of nilpotent Lie groups ⋮ \(\ell^p(\mathbb Z)\)-boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems ⋮ $L^p$ boundedness of discrete singular Radon transforms ⋮ An introduction to the circle method of Hardy, Littlewood, and Ramanujan ⋮ Two discrete fractional integral operators revisited ⋮ Jump inequalities for translation-invariant operators of Radon type on \(\mathbb{Z}^d\) ⋮ Schrödinger equation and oscillatory Hilbert transforms of second degree ⋮ Pseudo-differential operators on \(\mathbb{Z}^n\) with applications to discrete fractional integral operators ⋮ Discrete harmonic analysis associated with ultraspherical expansions ⋮ Discrete analogues in harmonic analysis. II: Fractional integration ⋮ Multiplication operators on some Morrey spaces ⋮ A sparse equidistribution result for $(\operatorname {SL}(2,\mathbb {R})/\Gamma _0)^{n}$ ⋮ Oscillation estimates for truncated singular Radon operators
Cites Work
- Estimates for singular convolution operators on the Heisenberg group
- Harmonic analysis on nilpotent groups and singular integrals. I: Oscillatory integrals
- On the maximal ergodic theorem for certain subsets of the integers
- Hilbert integrals, singular integrals, and Radon transforms. II
- On convergence and growth of partial sums of Fourier series
- Convergence almost everywhere of certain singular integrals and multiple Fourier series
- Problems in harmonic analysis related to curvature
- Bounds for exponential sums
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