TWO-WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS
نویسندگان
چکیده
We establish some equivalent conditions for a homeomorphism $$\varphi : D\rightarrow D'$$ of Euclidean domains in $$\mathbb R^n$$ , $$n\ge 2$$ to induce bounded composition operator ^*: {L}^1_p(D';\omega ) \cap \text {Lip}_l(D')\rightarrow L^1_q(D;\theta )$$ where $$1< q \le p<\infty$$ by the rule: ^*(f)=f\circ \varphi$$ . Here $$\omega :D'\rightarrow (0,\infty is an arbitrary weight function on domain $$D'$$ and $$\theta :D\rightarrow Muckenhoupt’s $$A_{q}$$ -class D. Moreover, we prove that class homeomorphisms under consideration completely determined controlled variation weighted capacity cubical condensers whose shells are concentric cubes.
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-05903-y