Results 1  10
of
18
Multilinear singular operators with fractional rank
 Pacific J. Math
"... Abstract. We prove bounds for multilinear operators on R d given by multipliers which are singular along a k dimensional subspace. The new case of interest is when the rank k/d is not an integer. Connections with the concept of true complexity from Additive Combinatorics are also investigated. ..."
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Abstract. We prove bounds for multilinear operators on R d given by multipliers which are singular along a k dimensional subspace. The new case of interest is when the rank k/d is not an integer. Connections with the concept of true complexity from Additive Combinatorics are also investigated.
A T(1) THEOREM FOR ENTANGLED MULTILINEAR DYADIC CALDERÓNZYGMUND OPERATORS
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ON SOME MAXIMAL MULTIPLIERS IN L p
, 2009
"... We extend an L 2 maximal multiplier result of Bourgain to all L p spaces, 1 < p < ∞. ..."
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We extend an L 2 maximal multiplier result of Bourgain to all L p spaces, 1 < p < ∞.
ON CURVATURE AND THE BILINEAR MULTIPLIER PROBLEM
, 907
"... Abstract. We provide sufficient normal curvature conditions on the boundary of a domain D ⊂ R4 to guarantee unboundedness of the bilinear Fourier multiplier operator TD with symbol χD outside the local L2 setting, i.e. from Lp1(R2) × Lp2(R2) → Lp ′ 3(R2) with P 1 = 1 and pj < 2 for some j. In p ..."
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Abstract. We provide sufficient normal curvature conditions on the boundary of a domain D ⊂ R4 to guarantee unboundedness of the bilinear Fourier multiplier operator TD with symbol χD outside the local L2 setting, i.e. from Lp1(R2) × Lp2(R2) → Lp ′ 3(R2) with P 1 = 1 and pj < 2 for some j. In pj particular, these curvature conditions are satisfied by any domain D that is locally strictly convex at a single boundary point. 1.
THE BILINEAR BOCHNERRIESZ PROBLEM
"... Abstract. Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear BochnerRiesz multipliers (1 − ξ  2 − η  2) δ + and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these mea ..."
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Abstract. Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear BochnerRiesz multipliers (1 − ξ  2 − η  2) δ + and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L 2 × L 2 into L 1 with minimal smoothness, i.e., any δ> 0, and we obtain estimates for other pairs of spaces for larger values of δ. Our study is broad enough to encompass general bilinear multipliers m(ξ, η) radial in ξ and η with minimal smoothness, measured in Sobolev space norms. The results obtained are based on a variety of techniques, that include Fourier series expansions, orthogonality, and bilinear restriction and extension theorems.