Bulletin of the London Mathematical Society最新文献

Let . The paper is devoted to the study of $��L^q�\to �L^p�$ estimates for transforms of noncommutative martingales, under the assumption that the transforming sequence takes values in $�L^r$, $��1�/�r�=�1�/�p�-�1�/�q�$. This goes beyond the usual context of $��p�=�q�$ and $��r�=�\infty �$ studied so far in the literature. The obtained constants are of optimal order at the endpoints, in addition the approach allows to obtain sharp values in the range $��p�⩽�2�⩽�q�$. The proof rests on real interpolation-type arguments for martingale transforms, which are of independent interest.

We introduce the notion of decoupling for operators, and prove an equivalence between classical $��{\ell }^q�L^p�$ decoupling for functions and $��{\ell }^q�S^p�$ decoupling for operators on bounded sets in $�R^{�2�d�}$. We also show that the equivalence depends only on the bounded set $�\Omega$ and not on the values of $��p�,�q�$ nor on the partition of $�\Omega$. The proof relies on a quantum version of Wiener's division lemma.

We give a description of the intersection of the zero set with the unit sphere of a polynomial that is zero-free in the unit ball of $�C^n$. This description leads to a necessary condition for a polynomial to be cyclic in Dirichlet-type spaces of the unit ball.

We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern Ricci-flat Hermitian metrics on several types of manifolds as well as a range of non-existence results for such metrics.

One way of defining the values of the modular $�j$-function at real quadratic irrationalities is by its cycle integrals along geodesics in the upper half plane whose endpoints are the roots of an indefinite binary quadratic form. We show that the restriction of the modular $�j$-function to Markov irrationalities (an important subset of real quadratic irrationalities in diophantine approximation) is continuous with respect to the topology induced by the euclidean norm.

A eutactic star on an integral lattice is called extremal if it induces a holomorphic Jacobi form of lattice index and singular weight via the theta block. The famous Macdonald identities imply that root systems are extremal as eutactic stars. In this paper, we prove that every extremal eutactic star arises as a root system. This answers a question posed by Skoruppa.

In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories enjoying covariant functors to categories of algebras given by constructions of path algebras, Cohn path algebras, and Leavitt path algebras, respectively. Thus, we obtain new tools to unravel homomorphisms between Leavitt path algebras and between graph C*-algebras. In particular, a graph-algebraic presentation of the inclusion of the C*-algebra of a quantum real projective plane into the Toeplitz algebra allows us to determine a quantum CW-complex structure of the former. It comes as a mixed-pullback theorem where two $�\ast$-homomorphisms are covariantly induced from path homomorphisms of graphs and the remaining two are contravariantly induced by admissible inclusions of graphs. As a main result and an application of new covariant-induction tools, we prove such a mixed-pullback theorem for arbitrary graphs whose all vertex-simple loops have exits, which substantially enlarges the scope of examples coming from noncommutative topology.

When $�k$ is a field, the classical Jacobian criterion computes the singular locus of an equidimensional, finitely generated $�k$-algebra as the closed subset of an ideal generated by appropriate minors of the so-called Jacobian matrix. Recently, Hochster-Jeffries and Saito have extended this result for algebras over any unramified discrete valuation ring of mixed characteristic via the use of $�p$-derivations. Motivated by these results, in this paper, we state and prove an analogous Jacobian criterion for algebras over ramified discrete valuation rings of mixed characteristic.

We prove a finiteness theorem for subgroups of bounded rank in hyperbolic 3-manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic 3-manifolds is a tower of finite covers associated to a fibration over a 1-orbifold.