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Bilinear estimates on Morrey spaces by using average. (English) Zbl 1463.42061

In this paper the author investigates the boundedness of the bilinear fractional integral operator. The author proves that the bilinear fractional integral operator is bounded from the product Morrey space \(\mathcal{M}^{p_{1}}_{q_{1}}(\mathbb{R}^n) \times \mathcal{M}^{p_{2}}_{q_{2}}(\mathbb{R}^n)\) to the Morrey space \(\mathcal{M}^{s}_{t}(\mathbb{R}^n)\) for \(0< \alpha < n,\ 1< q_{j} \leq p_{j} < \infty,\ j=1,2,\ 0 <t \leq 1 \leq s,\ \frac{1}{p} =\frac{1}{p_{1}}+ \frac{1}{p_{2}},\ \frac{1}{q}=\frac{1}{q_{1}}+\frac{1}{q_{2}},\ \frac{1}{s}=\frac{1}{p}-\frac{\alpha}{n},\ \frac{p}{q}=\frac{t}{s},\ s< \min(q_{1}, q_{2})\).

MSC:

42B35 Function spaces arising in harmonic analysis
42B25 Maximal functions, Littlewood-Paley theory
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References:

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