Let A be a bounded interval in R. Suppose we have a collection of functions, such that

1. Each function is $\in$ $L^r(A)$, where r is any number $\in$ $[1, \infty]$,

2. The fractional derivative of order 1/2 of the functions are bounded set in $L^2(A)$.

I want to know whether the set is precompact in $L^2(A) in the norm topology$?

Actually, I was reading a paper, it seems to me that the author assumed that this is correct. I think it might be a well-know fact in distribution theory. But I do not know the reference for the statement.

Let A be a bounded interval in R. Suppose we have a collection of functions, such that

1. Each function is $\in$ $L^r(A)$, where r is any number $\in$ $[1, \infty]$,

2. The fractional derivative of order 1/2 of the functions are bounded set in $L^2(A)$.

I want to know whether the set is precompact in $L^2(A)$ in the norm topology?

Actually, I was reading a paper, it seems to me that the author assumed that this is correct. I think it might be a well-know fact in distribution theory. But I do not know the reference for the statement.

Let A be a bounded interval in R. Suppose we have a collection of functions, such that

1. Each function is $\in$ $L^r(A)$, where r is any number $\in$ $[1, \infty]$,

2. The fractional derivative of order 1/2 of the functions are bounded set in $L^2(A)$.

I want to know whether the set is precompact in $L^2(A) in the norm topology$?

Actuall, I was reading a paper, it seems to me that the author assumed that this is correct. I think it might be a well-know fact in distribution theory. But I do not know the reference for the statement.

Let A be a bounded interval in R. Suppose we have a collection of functions, such that

1. Each function is $\in$ $L^r(A)$, where r is any number $\in$ $[1, \infty]$,

2. The fractional derivative of order 1/2 of the functions are bounded set in $L^2(A)$.

I want to know whether the set is precompact in $L^2(A) in the norm topology$?

Actually, I was reading a paper, it seems to me that the author assumed that this is correct. I think it might be a well-know fact in distribution theory. But I do not know the reference for the statement.

Let A be a bounded interval in R. Suppose we have a collection of functions, such that

1. Each function is $\in$ $L^r$, where r is any number $\in$ $[1, \infty]$,

2. The fractional derivative of order 1/2 of the functions are bounded set in $L^2$.

I wanna the set is precompact in $L^2$? Why?

Let A be a bounded interval in R. Suppose we have a collection of functions, such that

1. Each function is $\in$ $L^r(A)$, where r is any number $\in$ $[1, \infty]$,

2. The fractional derivative of order 1/2 of the functions are bounded set in $L^2(A)$.

I want to know whether the set is precompact in $L^2(A) in the norm topology$?

Actuall, I was reading a paper, it seems to me that the author assumed that this is correct. I think it might be a well-know fact in distribution theory. But I do not know the reference for the statement.