请教一个数学符号的含义
各位数学高手，请帮我看一下图片中标黄的这句话是什么意思？
前半句的意思是二元位移函数U在0到L的区间范围内是连续的？还是位移函数U在0到L的区间范围内是二阶可微的？亦惑是位移函数U的一阶导数和二阶导数在
0到L的区间范围内是连续的？后半句的意思是一元试函数N在0到L的区间范围内是连续的？还是试函数N在0到L的区间范围内是一阶可微的？亦惑是试函数N的一阶导数在0到L的区间范围内是连续的？
急盼各位的解答，有金币奖励奥！！！
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L2 is the function space whose element's square is integrable. H1 is a sobolev space, basically the function and it's first order weak derivative are in L2.
L2 is the function space whose element's square is integrable. H1 is a sobolev space, basically the function and it's first order weak derivative are in L2.
高手，你好！因为我没有学过泛函分析，所以再向你请教三个简单的问题。一、函数的平方可积，平方可积函数和二阶绝对可积函数三者在泛函分析中有没有区别，
L2到底属于这三者中的哪一个？二，H1到底是sobolev 空间还是 Hilbert空间，请高手指教？三、从图片英文的表述中，H1是怎么和L2联系起来的？十分感谢，必有重谢
，
1. The first and the second are the same, i.e. L2. The third one, I'm not sure, whether it means the absolute value function of the second order derivative is in L2.
2. H1 is both, since it's complete inner product space, that is Hilbert space. Here H1 is also with compact support. The test function has first order weak derivative but u doesn't necessarily have. After using Greens formula, the derivative of u will go to testing function
收到，谢谢！我怎么给你送感谢金币？
Doesn't matter. Thanks