In this paper we give the complete characterization of the boundedness of the generalized fractional maximal operator2010 Mathematics Subject Classification. 42B25, 42B35.

The aim of the paper is to calculate the norm of the generalized maximal operator M φ,Λ α (b) , defined with 0 < α < ∞ and functions b, φ : (0, ∞) → (0, ∞) for all measurable functions f on R n by 2010 Mathematics Subject Classification. 42B25, 42B35.

No abstract

The aim of the paper is to find the norm of the generalized maximal operator M ϕ,Λ α (b) , defined for all measurable functions f on R n , with 0 < α < ∞ and functions b, ϕ : (0, ∞) → (0, ∞), byQ∋x t 0 b(s) ds satisfies 0 < B(t) < ∞ for every t ∈ (0, ∞).