Complex interpolation of variable Triebel–Lizorkin spaces

Drihem, Douadi

doi:10.1016/j.na.2018.08.008

Cited by 2 publications

(2 citation statements)

References 23 publications

(66 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that, if p 0 , p 1 , p , λ 0 , λ 1 , λ are constants with

\frac{1}{p} = \frac{1 - θ}{p_{0}} + \frac{θ}{p_{1}}

and

λ_{0} = λ_{1} = λ

, then

{true[L^{p_{0}, λ_{0}}, L^{p_{1}, λ_{1}} true]}_{θ}

is the closure of

L^{p_{0}, λ_{0}} \cap L^{p_{1}, λ_{1}}

L^{p, λ}

and

{[L^{p_{0}, λ_{0}}, L^{p_{1}, λ_{1}}]}^{θ} = L^{p, λ}

. 3.If

λ (\cdot) = 0

and

p_{0} false(\cdot false)

and

p_{1} false(\cdot false)

are variable exponents, then our result is related to the complex interpolation of variable Lebesgue spaces, previously obtained in [6] (see also [7, 14]). In fact, Theorem 1.1 recaptures the results in [6].…”

Section: Introductionsupporting

confidence: 63%

See 1 more Smart Citation

Complex interpolation of variable Morrey spaces

Hakim

Sawano

2021

Mathematische Nachrichten

View full text Add to dashboard Cite

In this paper, we investigate the description of complex interpolation between variable Morrey spaces. We show that the first complex interpolation between variable Morrey spaces equals to certain closed subspaces of variable Morrey spaces. In addition, we prove that the second complex interpolation of variable Morrey spaces coincides with their intermediate spaces. Our proof uses the characterization of the Calderón product between variable Morrey spaces. Our results cover complex interpolation of variable Lebesgue spaces and complex interpolation of (classical) Morrey spaces.

show abstract

“…Recall that, if p 0 , p 1 , p , λ 0 , λ 1 , λ are constants with

\frac{1}{p} = \frac{1 - θ}{p_{0}} + \frac{θ}{p_{1}}

and

λ_{0} = λ_{1} = λ

, then

{true[L^{p_{0}, λ_{0}}, L^{p_{1}, λ_{1}} true]}_{θ}

is the closure of

L^{p_{0}, λ_{0}} \cap L^{p_{1}, λ_{1}}

L^{p, λ}

and

{[L^{p_{0}, λ_{0}}, L^{p_{1}, λ_{1}}]}^{θ} = L^{p, λ}

. 3.If

λ (\cdot) = 0

and

p_{0} false(\cdot false)

and

p_{1} false(\cdot false)

Section: Introductionsupporting

confidence: 63%

“…3. If 𝜆(⋅) = 0 and 𝑝 0 (⋅) and 𝑝 1 (⋅) are variable exponents, then our result is related to the complex interpolation of variable Lebesgue spaces, previously obtained in [6] (see also [7,14]). In fact, Theorem 1.1 recaptures the results in [6].…”

Section: Introductionsupporting

confidence: 57%