Correlation Inequalities in Function Spaces

Correlation Inequalities in Function Spaces

We give a condition for a Borel measure on R which is sufficient for the validity of an AD-type correlation inequality in the function space In [1] was proved that if φ1, φ2, φ3, φ4 are bounded real non negative measurable functions on the space with measure (Rn,B, μ) which satisfy for all x̄, ȳ ∈ R the following inequality φ1(x̄)φ2(ȳ) ≤ φ3(x̄ ∨ ȳ)φ4(x̄ ∧ ȳ) a.s., (1) then ∫ φ1(x̄)μ(dx̄) ∫ φ2(x̄)μ(dx̄)...

Hardy Inequalities in Function Spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces

In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|

Nikolskii-type Inequalities for Shift Invariant Function Spaces

Let Vn be a vectorspace of complex-valued functions defined on R of dimension n + 1 over C. We say that Vn is shift invariant (on R) if f ∈ Vn implies that fa ∈ Vn for every a ∈ R, where fa(x) := f(x− a) on R. In this note we prove the following. Theorem. Let Vn ⊂ C[a, b] be a shift invariant vectorspace of complex-valued functions defined on R of dimension n+ 1 over C. Let p ∈ (0, 2]. Then ‖f‖...