Complex interpolation of -spaces

Denny Ivanal Hakim; Shohei Nakamura; Yoshihiro Sawano; Takuya Sobukawa

doi:10.1080/17476933.2017.1327954

Complex interpolation of -spaces

Denny Ivanal Hakim^*, Shohei Nakamura, Yoshihiro Sawano, Takuya Sobukawa

^*Corresponding author for this work

Global Education Center

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The upper and lower complex interpolation of B^u_W(L^p)-spaces and B^u_W(M^p_q)-spaces are considered. When u₀, u₁ and u are finite, we prove that [B^u0_w0(L^p0), B^u1_w1(L^p1)]θ = [B^u0_w0(L^p0), B^u1_W1(L^p1)]^θ = B^u_W(L^p). Otherwise, the space [B^u0_w0(L^p0), B^u1_w1(L^p1)]θ is a closed subspace of B^u_W(L^p). We also establish interpolation results of certain closed subspaces of B^u_W(L^p)-spaces and B^u_W(M^p_q)-spaces, which are the closure of linear subspaces satisfying the lattice condition.

Original language	English
Pages (from-to)	569-590
Number of pages	22
Journal	Complex Variables and Elliptic Equations
Volume	63
Issue number	4
DOIs	https://doi.org/10.1080/17476933.2017.1327954
Publication status	Published - 2018 Apr 3

Keywords

complex interpolation
spaces

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1080/17476933.2017.1327954

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title = "Complex interpolation of -spaces",

abstract = "The upper and lower complex interpolation of BuW(Lp)-spaces and BuW(Mpq)-spaces are considered. When u0, u1 and u are finite, we prove that [Bu0w0(Lp0), Bu1w1(Lp1)]θ = [Bu0w0(Lp0), Bu1W1(Lp1)]θ = BuW(Lp). Otherwise, the space [Bu0w0(Lp0), Bu1w1(Lp1)]θ is a closed subspace of BuW(Lp). We also establish interpolation results of certain closed subspaces of BuW(Lp)-spaces and BuW(Mpq)-spaces, which are the closure of linear subspaces satisfying the lattice condition.",

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AU - Hakim, Denny Ivanal

AU - Nakamura, Shohei

AU - Sawano, Yoshihiro

AU - Sobukawa, Takuya

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Y1 - 2018/4/3

N2 - The upper and lower complex interpolation of BuW(Lp)-spaces and BuW(Mpq)-spaces are considered. When u0, u1 and u are finite, we prove that [Bu0w0(Lp0), Bu1w1(Lp1)]θ = [Bu0w0(Lp0), Bu1W1(Lp1)]θ = BuW(Lp). Otherwise, the space [Bu0w0(Lp0), Bu1w1(Lp1)]θ is a closed subspace of BuW(Lp). We also establish interpolation results of certain closed subspaces of BuW(Lp)-spaces and BuW(Mpq)-spaces, which are the closure of linear subspaces satisfying the lattice condition.

AB - The upper and lower complex interpolation of BuW(Lp)-spaces and BuW(Mpq)-spaces are considered. When u0, u1 and u are finite, we prove that [Bu0w0(Lp0), Bu1w1(Lp1)]θ = [Bu0w0(Lp0), Bu1W1(Lp1)]θ = BuW(Lp). Otherwise, the space [Bu0w0(Lp0), Bu1w1(Lp1)]θ is a closed subspace of BuW(Lp). We also establish interpolation results of certain closed subspaces of BuW(Lp)-spaces and BuW(Mpq)-spaces, which are the closure of linear subspaces satisfying the lattice condition.

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Complex interpolation of -spaces

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Keywords

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