Interpolation of Lorentz martingale spaces

Ren, Yanbo; Guo, Tiexin

doi:10.1007/s11425-012-4397-8

Cited by 6 publications

(2 citation statements)

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“…With the help of a new sharp maximal function and a new BMO space, Weisz identified the real interpolation spaces between martingale Hardy and BMO spaces in [26]. For more results about the real interpolation of martingale Hardy spaces, we refer to [12,[23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Real interpolation of variable martingale Hardy spaces and BMO spaces

Lü

Weisz

Zhou

2023

Banach J. Math. Anal.

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In this paper, we mainly consider the real interpolation spaces for variable Lebesgue spaces defined by the decreasing rearrangement function and for the corresponding martingale Hardy spaces. Let $$0<q\le \infty $$ 0 < q ≤ ∞ and $$0<\theta <1$$ 0 < θ < 1 . Our three main results are the following: $$\begin{aligned}{} & {} ({\mathcal {L}}_{p(\cdot )}({\mathbb {R}}^n),L_{\infty }({\mathbb {R}}^n))_{\theta ,q}={\mathcal {L}}_{{p(\cdot )}/(1-\theta ),q}({\mathbb {R}}^n),\\{} & {} ({\mathcal {H}}_{p(\cdot )}^s(\Omega ),H_{\infty }^s(\Omega ))_{\theta ,q}={\mathcal {H}}_{{p(\cdot )}/(1-\theta ),q}^s(\Omega ) \end{aligned}$$ ( L p ( · ) ( R n ) , L ∞ ( R n ) ) θ , q = L p ( · ) / ( 1 - θ ) , q ( R n ) , ( H p ( · ) s ( Ω ) , H ∞ s ( Ω ) ) θ , q = H p ( · ) / ( 1 - θ ) , q s ( Ω ) and $$\begin{aligned} ({\mathcal {H}}_{p(\cdot )}^s(\Omega ),BMO_2(\Omega ))_{\theta ,q}={\mathcal {H}}_{{p(\cdot )}/(1- \theta ),q}^s(\Omega ), \end{aligned}$$ ( H p ( · ) s ( Ω ) , B M O 2 ( Ω ) ) θ , q = H p ( · ) / ( 1 - θ ) , q s ( Ω ) , where the variable exponent $$p(\cdot )$$ p ( · ) is a measurable function.

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Section: Introductionmentioning

confidence: 99%

Real interpolation of variable martingale Hardy spaces and BMO spaces

Lü

Weisz

Zhou

2023

Banach J. Math. Anal.

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“…The reason we consider this topic is mainly based on two facts. The first one is that more and more attention has been paid to weak type spaces in harmonic analysis and martingale theory in many current researches, see for example in [2,6,[10][11][12][13][21][22][23][24]26,27]. In particular, Liu has carried out a series of excellent work on weak Orlicz spaces [16,18,19].…”

Section: Introductionmentioning

confidence: 99%