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The HardyLittlewood Maximal Theorem
WEAK TYPE INEQUALITIES FOR ITERATED OPERATORS
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A(nl Aag(s chapter class Rk constant independent containing the origin converge almost everywhere COROLLARY Differentiability of Multiple dominated convergence theorem Dunford and Schwartz everywhere in Q exists a finite f in Lp f in Rk_l f_fn finite interval finite measure space function f Hence Hglll I T(t)f dt implies independent of f individual ergodic theorem INEQUALITIES FOR ITERATED integrable function k-parameter k+l operators L(log+ last integral tends Lebesgue measure lemma Let us define lim inf Ll-function Ll+L Ll+Lm llflll log+ maximal ergodic operator maximal operator measurable functions measure zero measure-preserving transformations Mif(x multiple Lebesgue integrals N. M. Riviere non-negative function numbers Ogkgn PARAMETER SEMIGROUPS pointwise positive sublinear operator proof for i=1 real line representation of T(t)f scalar representation semigroup of measure-preserving sets xi+Ua(x simple functions strongly differentiable subadditive tends to zero theorem of Dunford vector space WEAK TYPE INEQUALITIES