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Strong-type endpoint obstructions for bilinear spherical maximal operators
For the bilinear spherical averages in dimension $d\geq2$, we show that the lacunary maximal operator is not bounded from $L^1(\mathbb R^d)\times L^q(\mathbb R^d)$ to $L^r(\mathbb R^d)$ whenever $1\leq q\leq\infty$ and $1/r=1+1/q$. The obstruction is realized by fixed nonnegative inputs; a second co
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