Kenneth Kunen (1943–) figured principally in the development of set theory in all the major directions, this during a formative period for the subject when it was transmuting to a sophisticated field of mathematics. In fact, several of Kunen’s results and proofs still frame modern set theory or serve as standards to be reckoned with in its further progress. This is all the more notable as much ...

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.

We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters; among them: (a) If m ≥ 1 and the ultrafilter D is (im(λ),im(λ))regular then D is κ-decomposable for some κ with λ ≤ κ ≤ 2 (Theorem 4.3(a)). (b) If λ is a strong limit cardinal and D is (im(λ ),im(λ ))regular then either D is (cf λ, cf λ)-regular or there are arbitrarily large κ < λ for which D is κ-decom...

We show that the L(w) operator norm of the composition M◦TΩ, where M is the maximal operator and TΩ is a rough homogeneous singular integral with angular part Ω ∈ L∞(Sn−1), depends quadratically on [w]A2 , and this dependence is sharp.

We study the splitting behaviour of quasilinear p-forms in the spirit of the theory of non-singular quadratic forms over fields of characteristic different from 2 using an analogue of Knebusch’s generic splitting tower. Several new applications to the theory of quasilinear quadratic forms are given. Among them, we can mention an algebraic analogue of Vishik’s theorem on ‘outer excellent connect...

Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν adds a generic for the Cohen forcing notion on ν. The following question (problem 5.1 in Miller’s list [Mi91]) is attributed to Rene David and Sy Friedman: Does the product of the forcing notions n2 add a generic for the forcing ω+12? We show here that the answer is ye...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...

We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let φ : C̃ → C be an unramified morphism of non-singular plane projective curves defined over a number field K. We calculate an effective upper bound for the norm of the relative discriminant of the number field K(Q) over K for any point P ∈ C(K) and Q ∈ φ(P ). 2000 MCS: 14G25, 14H25, 11G30.

We present results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps. We also prove that every isomorphism of such Lie algebras induces diffeomorphism of base manifolds respecting the generalized foliations defined by the anchor maps.

In this paper we give sufficient conditions on pair of weights (w, v) for some one-sided operators to be bounded from Lp(vp) to Lp(wp). The operators we deal with include the one-sided fractional maximal operator and the one-sided singular integrals. For the first operator necessary and sufficient conditions are knwon (see [MT], [LT]). These conditions usually amount to check the boundedness of...