Theoretical analysis reveals sufficient two-weight conditions for generalized translate maximal operator boundedness in weighted Lebesgue spaces, suggesting refined extensions of Muckenhoupt theory.
Let 1 < p < ∞ and w, v be two non-negative weight functions. In this paper, we provide a sufficient condition on w, v for the new maximal operator associated with the generalized translate operator Ty for each to be bounded from Lp,γ (v) to Lp,γ (w). Our condition is stronger, but closely related, to Muckenhoupt’s condition for two weights.
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A.Burcu Özyurt Serim (2026) studied this question.
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