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We obtain a local two weight $Tb$ theorem with an energy side condition forhigher dimensional fractional Calder\'{o}n-Zygmund operators. The proof followsthe general outline of the proof for the corresponding one-dimensional $Tb$theorem in [SaShUr12], but encountering a number of new challenges, includingseveral arising from the failure in higher dimensions of T. Hyt\"{o}nen'sone-dimensional two weight $A_{2}$ inequality [Hyt].

A two weight local $Tb$ theorem for $n$-dimensional fractional singular integrals