A T1 theorem for weakly singular integral operators
Vähäkangas, Antti V.
Original · EN
We establish conditions in the spirit of the T1 theorem of David and Journé which guarantee the boundedness of ∇ T on Lᵖ(ⁿ), where T is an integral transformation and 1<p<∞. These are natural size and regularity conditions for the kernel of the integral transformation, along with the sharp condition T1,Tᵗ1¹(BMO). A simple example satisfying these conditions is the Riesz potential denoted by I¹.
English translation
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