A generalization of Bourgain’s circular maximal theorem

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Abstract

For 0 < δ < 12, 1 < r < 2, and f ∈ S define C(x, r) = {y ∈ R2: |x − y | = r}, Cδ(x, r) = {y ∈ R2: r(1 − δ) < |x − y | < r(1 + δ)},

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Wilhelm Schlag (1997) studied this question.

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For 0 < δ < 12, 1 < r < 2, and f ∈ S define C(x, r) = {y ∈ R2: |x − y | = r}, Cδ(x, r) = {y ∈ R2: r(1 − δ) < |x − y | < r(1 + δ)},