Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L p -estimates for the heat semigroup on differential forms, and related
  problems   We consider a complete non-compact Riemannian manifold satisfying the volume
doubling property and a Gaussian upper bound for its heat kernel (on
functions). Let -- $\rightarrow$ $\Delta$ k be the Hodge-de Rham Laplacian on
differential k-forms with k $\ge$ 1. By the Bochner decomposition formula --
$\rightarrow$ $\Delta$ k = * + R k. Under the assumption that the negative part
R -- k is in an enlarged Kato class, we prove that for all p $\in$ [1,
$\infty$], e --t -- $\rightarrow$ $\Delta$ k p--p $\le$ C(t log t) D 4 (1-- 2
p) (for large t). This estimate can be improved if R -- k is strongly
sub-critical. In general, (e --t -- $\rightarrow$ $\Delta$ k) t>0 is not
uniformly bounded on L p for any p = 2. We also prove the gradient estimate e
--t$\Delta$ p--p $\le$ Ct -- 1 p , where $\Delta$ is the Laplace-Beltrami
operator (acting on functions). Finally we discuss heat kernel bounds on forms
and the Riesz transform on L p for p > 2.

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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an