if I know that a function f &#x2208; L 2 ( R d ) is supported in a compact ball in R d , how do I prove it is in L 1 ( R d )From the square integrability I know thatfor some constant C, then I know that f ( s u p p ( f ) ) is bounded, I need to show that it is closed as well to conclude that it is compact, but that will not be true in general if f is not continuous.How am I supposed to start given what I have?

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if I know that a function   f  &amp;#x2208;      L          2        (            R              d        ) is supported in a compact ball in             R              d      , how do I prove it is in       L          1        (            R              d        )From the square integrability I know thatfor some constant   C, then I know that   f  (  s  u  p  p  (  f  )  ) is bounded, I need to show that it is closed as well to conclude that it is compact, but that will not be true in general if   f is not continuous.How am I supposed to start given what I have?

Braedon Rivas · Accepted Answer

MathJax(?): Can&#039;t find handler for document  MathJax(?): Can&#039;t find handler for document  WLOG, assume   f  &amp;#x2265;  0, let   X  =      f          &amp;#x2212;      1        (  [  1  ,  &amp;#x221E;  )  ). Then,

pokoljitef2 · Accepted Answer

MathJax(?): Can&#039;t find handler for document MathJax(?): Can&#039;t find handler for document By using Holder&amp;#39;s inequality,

if I know that a function f ∈ L <mrow class="MJX-TeXAtom-ORD">

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