Currently displaying 1 – 9 of 9

Showing per page

Order by Relevance | Title | Year of publication

Gorenstein dimension of abelian categories arising from cluster tilting subcategories

Yu LiuPanyue Zhou — 2021

Czechoslovak Mathematical Journal

Let 𝒞 be a triangulated category and 𝒳 be a cluster tilting subcategory of 𝒞 . Koenig and Zhu showed that the quotient category 𝒞 / 𝒳 is Gorenstein of Gorenstein dimension at most one. But this is not always true when 𝒞 becomes an exact category. The notion of an extriangulated category was introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. Now let 𝒞 be an extriangulated category with enough projectives and enough injectives, and 𝒳 a cluster...

Bilinear operators associated with Schrödinger operators

Chin-Cheng LinYing-Chieh LinHeping LiuYu Liu — 2011

Studia Mathematica

Let L = -Δ + V be a Schrödinger operator in d and H ¹ L ( d ) be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by T ± ( f , g ) ( x ) = ( T f ) ( x ) ( T g ) ( x ) ± ( T f ) ( x ) ( T g ) ( x ) , where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from L p ( d ) × L q ( d ) to H ¹ L ( d ) for 1 < p,q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.

Some estimates for commutators of Riesz transform associated with Schrödinger type operators

Yu LiuJing ZhangJie-Lai ShengLi-Juan Wang — 2016

Czechoslovak Mathematical Journal

Let 1 = - Δ + V be a Schrödinger operator and let 2 = ( - Δ ) 2 + V 2 be a Schrödinger type operator on n ( n 5 ) , where V 0 is a nonnegative potential belonging to certain reverse Hölder class B s for s n / 2 . The Hardy type space H 2 1 is defined in terms of the maximal function with respect to the semigroup { e - t 2 } and it is identical to the Hardy space H 1 1 established by Dziubański and Zienkiewicz. In this article, we prove the L p -boundedness of the commutator b = b f - ( b f ) generated by the Riesz transform = 2 2 - 1 / 2 , where b BMO θ ( ρ ) , which is larger than the...

On sets of polynomials whose difference set contains no squares

Thái Hoàng LêYu-Ru Liu — 2013

Acta Arithmetica

Let q [ t ] be the polynomial ring over the finite field q , and let N be the subset of q [ t ] containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set A N for which A-A contains no squares of polynomials. By combining the polynomial Hardy-Littlewood circle method with the density increment technology developed by Pintz, Steiger and Szemerédi, we prove that D ( N ) q N ( l o g N ) 7 / N .

Page 1

Download Results (CSV)