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We study a family of Fourier integral operators by allowing their symbols to satisfy a multi-parameter differential inequality on RN. We show that these operators of order - (N-1) /2 are bounded from classical, atom decomposable H¹-Hardy space to L¹ (RN). Consequently, we obtain a sharp Lᵖ-regularity result due to Seeger, Sogge and Stein.
Tan et al. (Sun,) studied this question.
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