49 citations · 97 across the 17 of their papers we have counts for
17 papers
Best bounds for the dual Hardy operator minus identity on decreasing functions
Achraf Ben Said, Gord Sinnamon
The distance from the identity operator to , the dual of the Hardy averaging operator, is studied on the cone of nonnegative, nonincreasing functions in Lebesgue space. Th…
A Christ-Kiselev maximal theorem in quasi-Banach function lattices
Mieczysław Mastyło, Gord Sinnamon
A Christ-Kiselev maximal theorem is proved for linear operators between quasi-Banach function lattices satisfying certain lattice geometrical conditions. The result is further expl…
Core Decreasing Functions
Alejandro Santacruz Hidalgo, Gord Sinnamon
Given a measure space and a totally ordered ordered collection of measurable sets, called an ordered core, the notion of a core decreasing function is introduced and used to define…
The Fourier transform in weighted rearrangement invariant spaces
Mieczysław Mastyło, Gord Sinnamon
It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on , modified by a weight, then the weight is bounded above…
End-point Norm Estimates for Cesàro and Copson Operators
Sorina Barza, Bizuneh Minda Demissie, Gord Sinnamon
For a large class of operators acting between weighted spaces, exact formulas are given for their norms and the norms of their restrictions to the cones of nonnegativ…
Norm of the discrete Cesàro operator minus identity
Gord Sinnamon
The norm of on , where is the Cesàro operator, is shown to be when . This verifies a recent conjecture of G. J. O. Jameson. The norm of o…
Hardy inequalities in normal form
Gord Sinnamon
A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given t…
Revisiting a sharpened version of Hadamard's determinant inequality
Minghua Lin, Gord Sinnamon
Hadamard's determinant inequality was refined and generalized by Zhang and Yang in [Acta Math. Appl. Sinica 20 (1997) 269-274]. Some special cases of the result were rediscovered r…
Angular equivalence of normed spaces
Eder Kikianty, Gord Sinnamon
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of…
Power majorization between the roots of two polynomials
Minghua Lin, Gord Sinnamon
It is shown that if two hyperbolic polynomials have a particular factorization into quadratics, then their roots satisfy a power majorization relation whenever key coefficients in…
A New Algorithm for Approximating the Least Concave Majorant
Martin Franců, Ron Kerman, Gord Sinnamon
The least concave majorant, , of a continuous function on a closed interval, , is defined by \[ \hat F (x) = \inf \left\{ G(x): G \geq F, G \mbox{ concave}\right\},\…
Weighted Fourier inequalities via rearrangements
Javad Rastegari, Gord Sinnamon
The method of using rearrangements to give sufficient conditions for Fourier inequalities between weighted Lebesgue spaces is revisited. New results in the case q < p are establish…
Product operators on mixed norm spaces
Wayne Grey, Gord Sinnamon
Inequalities for product operators on mixed norm Lebesgue spaces and permuted mixed norm Lebesgue spaces are established. They depend only on inequalities for the factors and on th…
Calderón-Mityagin couples of Banach spaces related to decreasing functions
Mieczysław Mastyło, Gord Sinnamon
A number of Calderón-Mityagin couples and relative Calderón-Mityagin pairs are identified among Banach function spaces defined in terms of the least decreasing majorant constructio…
Fourier series in weighted Lorentz spaces
Javad Rastegari, Gord Sinnamon
The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, nec…
The D-topology for diffeological spaces
J. Daniel Christensen, Gord Sinnamon, Enxin Wu
Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural…
The Generalized Wielandt Inequality in Inner Product Spaces
Minghua Lin, Gord Sinnamon
A new inequality between angles in inner product spaces is formulated and proved. It leads directly to a concise statement and proof of the generalized Wielandt inequality, includi…