The Mihlin Multiplier Theorem on Anisotropic Mixed-Norm Hardy Spaces

Bilinear Θ$\Theta$‐type Calderón–Zygmund operators and their commutators on product generalized fractional mixed Morrey spaces

“…Proof of Theorem 1.8. Let 𝐵 = 𝐵(𝑥, 𝑟) be the open ball centered at 𝑥 ∈ 𝐑 𝑛 with radius 𝑟 > 0, and decompose functions 𝑓 𝑖 using the same form in Equation (17), that is,…”

“…In 2023, Lu and Tao [31] obtained the definition of a generalized fractional mixed Morrey spaces 𝐿 ⃗ 𝑝,𝜂,𝜑 (𝐑 𝑛 ), and prove that the Calderón-Zygmund integral operators 𝑇, the fractional integral operators 𝐼 𝛼 , and their corresponding commutators are bounded on spaces 𝐿 ⃗ 𝑝,𝜂,𝜑 (𝐑 𝑛 ) for 1 < ⃗ 𝑝 < ∞. Meanwhile, Huang [17] obtained a Mihlin multiplier theorem on anisotropic Hardy spaces 𝐻 ⃗ 𝑝 𝐴 (𝐑 𝑛 ) associated with a dilation matrix 𝐴. Other researches on the mixed-norm spaces can be seen in [5, 6, 19-21, 23, 26].…”