Let µ bea Borei measure on ℝd which may be non doubling. The only condition that µ must satisfy is µ(Q) ≤ c₀l(Q)n for any cube Q ⊂ ℝd with sides parallel to the coordinate axes and for some fixed n ...
Non-homogeneous metric measure spaces provide a versatile framework for extending classical harmonic analysis to settings where the underlying measure does not satisfy the usual doubling property.
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