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Lebesgue spaces

1978
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The Lebesgue spaces

1996
Let M be a measure space and 1 ≤ p ≤ ∞. A real-valued function f on M is said to be pth-power integrable, or belong to L p , if f is measurable, and |f| p is integrable if p < ∞, while if p = ∞, it is required that there exist a null set in M on whose complement f is bounded.
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Bessel-Riesz Operators on Lebesgue Spaces with Lebesgue Measures

Malaysian Journal of Mathematical Sciences
This study investigates a class of mathematical operators known as the Bessel-Riesz operators, defined in Euclidean space Rn, given by, Tμ,νf(z) =Z Rn Kμ,ν (|z − w|)f(w)dν(w), for z ∈ Rn. (1) Here, Kμ,ν is called the Bessel-Riesz kernel. It can be expressed as a multiple of the Bessel kernel Jν and the Riesz kernel Kμ.
S. Mehmood   +3 more
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Bernoulli Maps of a Lebesgue Space

Canadian Mathematical Bulletin, 1988
AbstractA collection of measure preserving mappings having Bernoulli generators is considered. Only three conditions are required to be satisfied, and they are quite easy to check.
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Endomorphisms of a Lebesgue space III

Israel Journal of Mathematics, 1975
A new invariant is introduced for regular isomorphisms, which are isomorphisms by codes that anticipate a finite amount of the future. With the help of this invariant it is shown that the Bernoulli automorphism (p, q) is not regularly isomorphic to the Markov automorphism (
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Variable Lebesgue Spaces

2013
This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with ...
CRUZ URIBE D., FIORENZA, ALBERTO
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