Related papers: A T(1) theorem on product spaces

The restoration of an additive function defined on P parallelepipeds via its derivative with respect to P parallelepipeds is studied. The obtained theorem is applied to the questions of uniqueness of multiple series with regard to Haar and…

We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…

We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.

We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type $A_{n-1}$. As a special case, the corresponding constant term conjecture is also proved.

We complete our theory of weighted $L^p(w_1) \times L^q(w_2) \to L^r(w_1^{r/p} w_2^{r/q})$ estimates for bilinear bi-parameter Calder\'on--Zygmund operators under the assumption that $w_1 \in A_p$ and $w_2 \in A_q$ are bi-parameter weights.…

In this paper we extend dyadic shifts and the dyadic representation theorem to an operator-valued setting: We first define operator-valued dyadic shifts and prove that they are bounded. We then extend the dyadic representation theorem,…

We prove a basic result about tensor products of a $\text{II}_1$ factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.

We prove that there are exactly five sequences, including the triangular numbers, that satisfy the product rule $T(mn) = T(m) T(n) + T(m-1) T(n-1)$ for all $m, n \ge 1$.

I provide an alternate and self-contained proof of Botha's theorem on products of idempotent and square-zero matrices where the product contains two square-zero factors, and provide a conclusive characterisation of products of singular…

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

For multiparameter bilinear paraproduct operators $B$ we prove the estimate $$ B: L^p X L^q --> L^r, 1<p,q\le{}\infty. $$ Here, $1/p+1/q=1/r$ and special attention is paid to the case of $0<r<1$. (Note that the families of multiparameter…

We prove a wavelet $T(1)$ theorem for compactness of multilinear Calder\'{o}n-Zygmund (CZ) operators. Our approach characterizes compactness in terms of testing conditions and yields a representation theorem for compact CZ forms in terms of…

We prove a maximality theorem for one-parameter dynamical systems including multiplier one-parameter dynamical systems. Our main result is new even for one-parameter actions on commutative multiplier algebras including the algebra of…

We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.

By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.

We show that there are six different choice of tensor product of supersymmetric N=(1,1) spectral data in the context of supersymmetric quantum theory and noncommutative geometry. We also show that the procedure of extending a supersymmetric…

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…

A prime geodesic theorem for singular geodesics in a locally symmetric space is proved. As an application, an asymptotic formula for units in number fields is given.

We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals…