Multilinear generalized Radon transforms and point configurations
-
Loukas Grafakos
,
Allan Greenleaf
Abstract
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case.
These provide a general mechanism to study Falconer-type problems involving (k+1)-point configurations in geometric measure theory, with k ≥ 2, including the distribution of simplices, volumes and angles determined by the points of
fractal subsets E ⊂ ℝd, d ≥ 2.
If Tk(E) denotes the set of noncongruent
Funding source: NSF
Award Identifier / Grant number: DMS 0900946
Funding source: NSF
Award Identifier / Grant number: DMS 0853892
Funding source: NSF
Award Identifier / Grant number: DMS 1045404
We would like to thank an anonymous referee for recommending expository improvements.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Notes on occupation time fluctuations of binary branching particle systems
- On the sum of two integral squares in certain quadratic fields
- A Cesàro average of Goldbach numbers
- Groups described by element numbers
- The second main theorem for entire curves into Hilbert modular surfaces
- L∞ norms of holomorphic modular forms in the case of compact quotient
- SU(2)-Donaldson invariants of the complex projective plane
- Pairs of diagonal quadratic forms and linear correlations among sums of two squares
- The subelliptic heat kernel on the three-dimensional solvable Lie groups
- Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
- Circle-valued Morse theory for complex hyperplane arrangements
- Atomic Hp spaces and their duals on open subsets of ℝd
- Locally contractible coset spaces
- L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
- Finite time blow-up for semilinear wave equations with variable coefficients
- Intertwining operators of irreducible representations for exponential solvable Lie groups
- Artin's conjecture and systems of diagonal equations
- The homology of simplicial complements and the cohomology of polyhedral products
- Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
- Multilinear generalized Radon transforms and point configurations
- On ratios of Petersson norms for Yoshida lifts
- K-groups for rings of finite Cohen–Macaulay type
- Character degree sums of finite groups
- Tame Fréchet submanifolds of co-Banach type
- Weighted norm inequalities for Schrödinger type operators
Articles in the same Issue
- Frontmatter
- Notes on occupation time fluctuations of binary branching particle systems
- On the sum of two integral squares in certain quadratic fields
- A Cesàro average of Goldbach numbers
- Groups described by element numbers
- The second main theorem for entire curves into Hilbert modular surfaces
- L∞ norms of holomorphic modular forms in the case of compact quotient
- SU(2)-Donaldson invariants of the complex projective plane
- Pairs of diagonal quadratic forms and linear correlations among sums of two squares
- The subelliptic heat kernel on the three-dimensional solvable Lie groups
- Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
- Circle-valued Morse theory for complex hyperplane arrangements
- Atomic Hp spaces and their duals on open subsets of ℝd
- Locally contractible coset spaces
- L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
- Finite time blow-up for semilinear wave equations with variable coefficients
- Intertwining operators of irreducible representations for exponential solvable Lie groups
- Artin's conjecture and systems of diagonal equations
- The homology of simplicial complements and the cohomology of polyhedral products
- Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
- Multilinear generalized Radon transforms and point configurations
- On ratios of Petersson norms for Yoshida lifts
- K-groups for rings of finite Cohen–Macaulay type
- Character degree sums of finite groups
- Tame Fréchet submanifolds of co-Banach type
- Weighted norm inequalities for Schrödinger type operators
