Psalm 16:9-10 speaks about Jesus? Paul and Peter caught lying

Psa 16:9  Therefore my heart is glad, and my glory rejoiceth: my flesh also shall rest in hope. 
Psa 16:10  For thou wilt not leave my soul in hell; neither wilt thou suffer thine Holy One to see corruption. 

Act 2:27  Because thou wilt not leave my soul in hell, neither wilt thou suffer thine Holy One to see corruption. 
Act 2:28  Thou hast made known to me the ways of life; thou shalt make me full of joy with thy countenance. 
Act 2:29  Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day. 
Act 2:30  Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne; 
Act 2:31  He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption. 

Act 13:35  Wherefore he saith also in another psalm, Thou shalt not suffer thine Holy One to see corruption. 
Act 13:36  For David, after he had served his own generation by the will of God, fell on sleep, and was laid unto his fathers, and saw corruption: 
Act 13:37  But he, whom God raised again, saw no corruption. 

Analysis: The hebrew word "therefore" concludes verses 1-8 and in that conclusion the psalmist exalts the Lord by putting his trust in him. (Psa 16:8  I have set the LORD always before me: because he is at my right hand, I shall not be moved.)

The psalmist is talking about another person in this psalm? No. Because he particularizes "his own person" using the following words in verse 9: "my heart", "my glory", "my flesh".

The word "for" in verse 10 is a explanatory conjunction, ie, his confidence in the Lord was so great that even being in the Sheol, the Lord would not abandon him, he would not left him in the power of Sheol but would remain with him.

The same characteristic structure is found in verse 10 with the following words "my soul", "thine holy one (saint)". Nothing in this verse specially refers to Jesus.

Another point to be analysed is the word shachath (the christian bible translates as "corruption" and christians say it is about a deteriorated body) which is not abstract to give a sense of "corruption", no. The word is concrete with the meaning of "pit" being synonymous of Sheol, usually understood as another proper name of Sheol like a "well" or "cave" under the earth; but the use favors the opinion that it is a well in the Sheol, as a deeper place of Sheol being also synonymous of Abadon, the dungeon of Sheol.

What the psalmist means with that? He says that he will see the Sheol, but will not be abandoned there; he won't see the dungeon of Sheol, the place of the wicked. The psalmist has hope, expectation and trust of the presence and the grace of God after his death.