Can we use "these days" with the present perfect?

Which sentence is grammatically correct?

"I've been really busy these days"

OR

"I'm really busy these days"

I may be wrong but for some reason it feels funny to use "these days" with the present perfect tense since, to me, "I've been really busy" implies that "I'm not that busy anymore", which is in contrast with what the phrase "these days" implies (= "I'm still busy"). Am I wrong?

P.S. I have asked this question to some native speakers of English and I got some contradictory answers. Could it be a regional thing?

Solution 1:

According to OALD this expression is used to speak about the present, that is, an ongoing present, taken to begin a little before true present and considered to continue similarly in the future.

• (informal) used to talk about the present, especially when you are comparing it with the past
  These days kids grow up so quickly.

Solution 2:

The term these days is informal enough that its meaning can be stretched slightly to mean recently as well as the dictionary definitions of now or at present. Obviously

I've been really busy now

would be incorrect, but

I've been really busy recently

is fine. Pedants may insist on the dictionary definitions, which would constrain it use, but

I've been really busy these days

seems to be acceptable to me. One can easily infer the intended meaning from the tense of the verb.

Solution 3:

"These days" is an adverbial phrase and equivalent to "lately/recently". If you can say "lately/recently", you can say "these days".