The paper extends the Sobolev-type inequalities of Guo-Phong-Song-Sturm and Guedj-Tô from functions to twisted differential forms using heat kernel estimates.
Davies, Heat kernels and spectral theory, Cambridge Tracts in Mathematics, 92
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Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact K\"ahler manifolds
The paper extends the Sobolev-type inequalities of Guo-Phong-Song-Sturm and Guedj-Tô from functions to twisted differential forms using heat kernel estimates.