Abstract
AbstractIn this paper we consider nonnegative functions f on $$\mathbb {R}^n$$
R
n
which are defined either by $$f(x)=\min \,(f_1(x_1),\ldots ,f_n(x_n))$$
f
(
x
)
=
min
(
f
1
(
x
1
)
,
…
,
f
n
(
x
n
)
)
or by $$f(x)=\min \,(f_1(\hat{x}_1),\ldots ,f_n(\hat{x}_n)).$$
f
(
x
)
=
min
(
f
1
(
x
^
1
)
,
…
,
f
n
(
x
^
n
)
)
.
Such minimum-functions are useful, in particular, in embedding theorems. We prove sharp estimates of rearrangements and Lorentz type norms for these functions, and we find the link between their Lorentz norms and geometric properties of their level sets.
Publisher
Springer Science and Business Media LLC
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