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  1. ; ; ; (, International Mathematics Research Notices)
    null (Ed.)
    Abstract We show that the 1st-order Sobolev spaces $$W^{1,p}(\Omega _\psi ),$$  $$1<p\leq \infty ,$$ on cuspidal symmetric domains $$\Omega _\psi $$ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $$M^{1,p}(\Omega _\psi )$$. 
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  2. ; ; (, Journal of Functional Analysis)
    null (Ed.)
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  3. ; (, Advances in Mathematics)
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  4. ; (, Transactions of the American Mathematical Society)
    null (Ed.)
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  5. (, Annales Academiae Scientiarum Fennicae Mathematica)
    null (Ed.)
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  6. ; ; ; (, Advances in Calculus of Variations)
    Abstract We consider two notions of functions of bounded variation in complete metric measure spaces,one due to Martio and the other due to Miranda Jr. We show that these two notionscoincide if the measure is doubling and supports a 1-Poincaré inequality. In doing so, we also prove that if the measure is doubling and supports a 1-Poincaré inequality, then the metric space supports a Semmes family of curves structure. 
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