论文标题
真实插值方法的重申公式，包括限制$ {\ Mathcal L} $或$ {\ Mathcal R} $ space
Reiteration Formulae for the Real Interpolation Method Including limiting ${\mathcal L}$ or ${\mathcal R}$ Spaces
论文作者
论文摘要
我们考虑涉及缓慢变化功能的K交互方法。令$ \ Overline {a} _ {θ，*}^{\ Mathcal {l}} $和$ \ overline {a} _ {θ，*}，*}^{\ Mathcal {r}} $（0 \leqθ\ leq1）$是所谓的$ $ {\ MATHCAL {R}} $限制插值空间，这些空间自然而然地以限制案例的重复公式出现。我们表征了插值空间$ \ big（\ overline {a} _ {θ_0，*}^{\ Mathcal {l}}}，*\ big）_ {η，r，a} $，$ \ big（\ big big） *\ big）_ {η，r，a} $，$ \ big（*，\ overline {a} _ {θ_1，*}^}^{\ mathcal {l}} \ big）_ { \ edline {a} _ {θ_1，*}^{\ Mathcal {r}} \ big）_ {η，r，a} $ $（0 \ leq或leq leq1）$对于限制案例$θ_0= 0 = 0 $ and $θ_1= 0 $和$θ_1= 1 $。这补充了作者的早期论文，该论文仅考虑了$ 0 <θ_0<θ_1<1 $ $。大多数重申公式的证明是基于Holmstedt-type公式。给出了向大型和小洛伦兹空间以及洛伦兹 - 卡拉马塔人空间的应用。
We consider K-interpolation methods involving slowly varying functions. Let $\overline{A}_{θ,*}^{\mathcal{L}}$ and $\overline{A}_{θ,*}^{\mathcal{R}}$ $(0\leqθ\leq1)$ be the so called ${\mathcal{L}}$ or ${\mathcal{R}}$ limiting interpolation spaces which arise naturally in reiteration formulae for the limiting cases. We characterize the interpolation spaces $\Big(\overline{A}_{θ_0,*}^{\mathcal{L}}, *\Big)_{η,r,a}$, $\Big(\overline{A}_{θ_0,*}^{\mathcal{R}}, *\Big)_{η,r,a}$, $\Big(*, \overline{A}_{θ_1,*}^{\mathcal{L}}\Big)_{η,r,a}$, and $\Big(*, \overline{A}_{θ_1,*}^{\mathcal{R}}\Big)_{η,r,a}$ $(0\leqη\leq1)$ for the limiting cases $θ_0=0$ and $θ_1=1$. This supplements the earlier papers of the authors, which only considered the case $0<θ_0<θ_1<1$. The proofs of most reiteration formulae are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces as well as to Lorentz-Karamata spaces are given.
