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P-convexity of Musielak-Orlicz function spaces of Bochner type.

Pawel. Kolwicz, Ryszard Pluciennik (1998)

Revista Matemática Complutense

It is proved that the Musielak-Orlicz function space LF(mu,X) of Bochner type is P-convex if and only if both spaces LF(mu,R) and X are P-convex. In particular, the Lebesgue-Bochner space Lp(mu,X) is P-convex iff X is P-convex.

Points fixes et théorèmes ergodiques dans les espaces L¹(E)

Mourad Besbes (1992)

Studia Mathematica

We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.

Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations

Ryotaro Sato (1995)

Studia Mathematica

Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average n - 1 i = 0 n - 1 f τ i ( x ) converges almost everywhere to a function f* in L ( p 1 , q 1 ] , where (pq) and ( p 1 , q 1 ] are assumed to be in the set ( r , s ) : r = s = 1 , o r 1 < r < a n d 1 s , o r r = s = . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized and unified...

Pointwise multipliers on martingale Campanato spaces

Eiichi Nakai, Gaku Sadasue (2014)

Studia Mathematica

We introduce generalized Campanato spaces p , ϕ on a probability space (Ω,ℱ,P), where p ∈ [1,∞) and ϕ: (0,1] → (0,∞). If p = 1 and ϕ ≡ 1, then p , ϕ = B M O . We give a characterization of the set of all pointwise multipliers on p , ϕ .

Pointwise multipliers on weighted BMO spaces

Eiichi Nakai (1997)

Studia Mathematica

Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for ϕ : X × + + , we denote by b m o ϕ , p ( X ) the set of all functions f L l o c p ( X ) such that s u p a X , r > 0 1 / ϕ ( a , r ) ( 1 / μ ( B ( a , r ) ) ʃ B ( a , r ) | f ( x ) - f B ( a , r ) | p d μ ) 1 / p < , where B(a,r) is the ball centered at a and of...

Power means and the reverse Hölder inequality

Victor D. Didenko, Anatolii A. Korenovskyi (2011)

Studia Mathematica

Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means α w ( x ) : = ( ( 1 / x ) 0 x w α ( t ) d t ) 1 / α , x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.

Product spaces generated by bilinear maps and duality

Enrique A. Sánchez Pérez (2015)

Czechoslovak Mathematical Journal

In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise...

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