Hello Yasuhiko,
Here is an application note about some considerations and references to low power modes in Kinetis (http://cache.freescale.com/files/32bit/doc/app_note/AN4503.pdf).
In this application note, there is an specific section pointing out some Energy Saving Peripherals (Section 2.2 Energy Saving Peripherals), for example, for UART0, it can receive and transmit in VLPS mode and can use DMA to receive data and store in a buffer or viceversa with the core shutdown. Maybe you should look a this application note for more details.

As Carlos pointed before, you can also refer to section 11 Modules in Power modes in which table 5 explains status for different peripherals in low power modes:

This table sumarizes each peripheral behavior on every low power mode.
I hope this document can help you understand peripheral behavior in every low power mode.
Best Regards,
Isaac
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