Weak Type Inequalities for Iterated Operators |
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Contents
WEAK TYPE INEQUALITIES FOR ITERATED OPERATORS | 9 |
Application to Almost Everywhere Convergence of Multiple | 16 |
kPARAMETER SEMIGROUPS OF MEASUREPRESERVING | 31 |
Common terms and phrases
A(n₁ chapter consider constant independent containing the origin converge almost everywhere COROLLARY Differentiability of Multiple dominated convergence theorem Dunford and Schwartz exists a finite f in LP f in R-1 f(os finite interval finite measure follows Fubini's theorem function f g(log Hence i₁ independent of f individual ergodic theorem k-parameter semigroup last integral tends Lebesgue measure lemma Let us define lim inf lim sup linear operators M₁f(x M₂ M₂f(x maximal ergodic operator maximal operator measurable functions measure space measure zero measure-preserving transformations Mf(x multiple Lebesgue integrals N. M. Riviere non-negative function numbers pointwise prove scalar representation semigroup T(t sequence simple function SM₂ strongly differentiable subadditive tends to zero theorem of Dunford vector space WEAK TYPE INEQUALITIES x₁ µ(ds ΧΩ سية