<p>Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$(X,d,\mu )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>d</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be an RD-space satisfying the doubling condition in the sense of Coifman and Weiss and a certain reverse doubling condition. In this setting, the authors first investigate a weighted John–Nirenberg inequality for the space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\textrm{BMO}_{\theta ,\varphi }(X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>BMO</mtext> <mrow> <mi>θ</mi> <mo>,</mo> <mi>φ</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> introduced in Lu, G.; Wang, M.: Characterizations of spaces <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathrm BMO_{\theta ,\varphi }(X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">B</mi> <mi>M</mi> <msub> <mi>O</mi> <mrow> <mi>θ</mi> <mo>,</mo> <mi>φ</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> on RD-spaces., which extends some known results on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\textrm{BMO}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>BMO</mtext> </math></EquationSource> </InlineEquation>-type spaces on Euclidean spaces and RD-spaces. Furthermore, some useful characterizations of spaces <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\textrm{BMO}_{\theta ,\varphi }(X)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>BMO</mtext> <mrow> <mi>θ</mi> <mo>,</mo> <mi>φ</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> are established.</p>

Weighted John–Nirenberg inequality for spaces $\textrm{BMO}_{\theta ,\varphi }$ over RD-spaces

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发表日期：

2026年6月20日

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Guanghui Lu,
Miaomiao Wang

摘要

Let $(X,d,\mu )$ $(X, d, μ)$ be an RD-space satisfying the doubling condition in the sense of Coifman and Weiss and a certain reverse doubling condition. In this setting, the authors first investigate a weighted John–Nirenberg inequality for the space $\textrm{BMO}_{\theta ,\varphi }(X)$ ${BMO}_{θ, φ} (X)$ introduced in Lu, G.; Wang, M.: Characterizations of spaces $\mathrm BMO_{\theta ,\varphi }(X)$ $B M O_{θ, φ} (X)$ on RD-spaces., which extends some known results on $\textrm{BMO}$ $BMO$ -type spaces on Euclidean spaces and RD-spaces. Furthermore, some useful characterizations of spaces $\textrm{BMO}_{\theta ,\varphi }(X)$ ${BMO}_{θ, φ} (X)$ are established.

Weighted John–Nirenberg inequality for spaces \(\textrm{BMO}_{\theta ,\varphi }\) over RD-spaces

摘要