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372
L p estimates for the bilinear Hilbert transform
, 1996
"... For the bilinear Hilbert transform given by H fg(x) = p. v. Z f(x \Gamma y)g(x + y) dy y we announce the inequality kH fgk p3 K p1 ;p 2 kfk p1 kgk p2 , provided 2 ! p 1 ; p 2 ! 1, 1=p 3 = 1=p 1 + 1=p 2 and 1 ! p 3 ! 2. We announce a partial resolution to long standing conjectures concerning th ..."
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Cited by 62 (16 self)
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For the bilinear Hilbert transform given by H fg(x) = p. v. Z f(x \Gamma y)g(x + y) dy y we announce the inequality kH fgk p3 K p1 ;p 2 kfk p1 kgk p2 , provided 2 ! p 1 ; p 2 ! 1, 1=p 3 = 1=p 1 + 1=p 2 and 1 ! p 3 ! 2. We announce a partial resolution to long standing conjectures concerning
Uniform bounds for the bilinear Hilbert transforms
 889–993. MR2113017 (2006e:42011), Zbl 1071.44004. Xiaochun Li
, 2004
"... Abstract. We continue the investigation initiated in [8] of uniform Lp bounds � for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. f(x − αt)g(x − βt) R dt t. In this work we show that Hα,β map Lp1 (R) × Lp2 (R) into Lp (R) uniformly in the real parameters α, β satisfying  α β − 1  ..."
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Cited by 36 (15 self)
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Abstract. We continue the investigation initiated in [8] of uniform Lp bounds � for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. f(x − αt)g(x − βt) R dt t. In this work we show that Hα,β map Lp1 (R) × Lp2 (R) into Lp (R) uniformly in the real parameters α, β satisfying  α β − 1
Higherdimensional algebra II: 2Hilbert spaces
"... A 2Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we define a 2Hilbert space to be an abelian category enriched over Hilb with a ∗structure, conjugatelinear on the homsets, satisfying 〈fg,h 〉 = 〈g,f ∗ h 〉 = 〈f,hg ∗ 〉. We also ..."
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Cited by 58 (12 self)
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A 2Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we define a 2Hilbert space to be an abelian category enriched over Hilb with a ∗structure, conjugatelinear on the homsets, satisfying 〈fg,h 〉 = 〈g,f ∗ h 〉 = 〈f,hg ∗ 〉. We also
Hilbert modular forms and the Ramanujan conjecture
 IN “NONCOMMUTATIVE GEOMETRY AND NUMBER THEORY” ASPECTS OF MATHEMATICS E37, 35–56
, 2003
"... Let F be a totally real field. In this paper we study the Ramanujan Conjecture for Hilbert modular forms and the WeightMonodromy Conjecture for the Shimura varieties attached to quaternion algebras over F. As a consequence, we deduce, at all finite places of the field of definition, the full automo ..."
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Cited by 27 (0 self)
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Let F be a totally real field. In this paper we study the Ramanujan Conjecture for Hilbert modular forms and the WeightMonodromy Conjecture for the Shimura varieties attached to quaternion algebras over F. As a consequence, we deduce, at all finite places of the field of definition, the full
Series in Banach and Hilbert Spaces
, 1992
"... this paper. For simplicity, we adopt the following convention: X denotes a real unitary space, a, b, r denote real numbers, s 1 , s 2 , s 3 denote sequences of X , R 1 , R 2 , R 3 denote sequences of real numbers, and k, n, m denote natural numbers. The scheme Rec Func Ex RUS deals with a real unita ..."
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Cited by 1 (0 self)
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this paper. For simplicity, we adopt the following convention: X denotes a real unitary space, a, b, r denote real numbers, s 1 , s 2 , s 3 denote sequences of X , R 1 , R 2 , R 3 denote sequences of real numbers, and k, n, m denote natural numbers. The scheme Rec Func Ex RUS deals with a real
Hilbert 90 for Galois cohomology
, 2006
"... Abstract. Assuming the BlochKato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor ktheory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal pextension of F is at most n. The ..."
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Cited by 1 (1 self)
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Abstract. Assuming the BlochKato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor ktheory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal pextension of F is at most n
FAILURE OF AMALGAMATION IN HILBERT LATTICES
"... We show that Bruns and Harding’s counterexample (see [1]) to amalgamation in orthomodular lattices also works for Hilbert lattices. The argument is based on the example of a nonmodular Hilbert lattice devised by von Neumann in a letter to Birkhoff (see [2] for an extensive quotation from that lette ..."
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that letter). Consider the real sequence space `2 = {f: N+ → R: Σ∞i=1f(i)2 < ∞}, where N+ stands for N \ {0}. Let 〈en: n ∈ N+ 〉 be the standard orthonormal base of `2, i.e., en(n) = 1 and en(m) = 0 for m 6 = n. It follows from Satz 15 in [3] that there are two unbounded selfadjoint operators X and Y
Circular Peaks and Hilbert Series
, 2008
"... The circular peak set of a permutation σ is the set {σ(i)  σ(i−1) < σ(i)> σ(i+1)}. Let Pn be the set of all the subset S ⊆ [n] such that there exists a permutation σ which has the circular set S. We can make the set Pn into a poset Pn by defining S ≼ T if S ⊆ T as sets. In this paper, we pro ..."
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prove that the poset Pn is a simplicial complex on the vertex set [3,n]. We study the fvector, the fpolynomial, the reduced Euler characteristic, the Möbius function, the hvector and the hpolynomial of Pn. We also derive the zeta polynomial of Pn and give the formula for the number of the chains
NOTES ON THE ARITHMETIC OF HILBERT MODULAR FORMS
"... Shimura proved the following fundamental result (see [37, Theorem 4.3]) on the critical values of the standard Lfunction attached to a holomorphic Hilbert modular form. Theorem 1.1 (Shimura). Let f be a primitive holomorphic Hilbert modular cusp form of type (k, ψ) over a totally real number field ..."
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Cited by 7 (2 self)
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Shimura proved the following fundamental result (see [37, Theorem 4.3]) on the critical values of the standard Lfunction attached to a holomorphic Hilbert modular form. Theorem 1.1 (Shimura). Let f be a primitive holomorphic Hilbert modular cusp form of type (k, ψ) over a totally real number field
Hecke operators and Hilbert modular forms Hecke operators and Hilbert modular forms
"... Abstract. Let F be a real quadratic field with ring of integers Ø and with class number 1. Let Γ be a congruence subgroup of GL2(Ø). We describe a technique to compute the action of the Hecke operators on the cohomology H 3 (Γ ; C). For F real quadratic this cohomology group contains the cuspidal c ..."
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Abstract. Let F be a real quadratic field with ring of integers Ø and with class number 1. Let Γ be a congruence subgroup of GL2(Ø). We describe a technique to compute the action of the Hecke operators on the cohomology H 3 (Γ ; C). For F real quadratic this cohomology group contains the cuspidal
Results 1  10
of
372