Abstract
The class p Н λ of λ -means of the power expansions of analytic functions p H ∈ ϕ is constructed. The behavior of λ -means for tending of arbitrary point ) , ( r y of the circle to a point ) 1 , (x along non-tangential paths are studied. The estimates for the corresponding maximal operators and theorems of summability almost everywhere are established. The results for Hardy classes of functions are linked to performance p p p L i L Н λ λ λ ⊕ = ~ in which p L λ and p L λ ~ , respectively, are classes of λ -means of Fourier series and conjugate series of ϕ = Re f .
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