In this paper, we obtain the Lp(ℝ²)-boundedness of the maximal functions M I,γ f x 1 , x 2 := sup j∈ℤ sup ε>0 1 2ε ∫ –ε ε f x 1 –t, x 2 – 2 j γ(t) dt and M II,γ f x 1 , x 2 := sup i,j∈ℤ sup ε>0 1 2ε ∫ ...
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