Jamieson, Fausset and Brown on Isaiah 7:11

11. Ask thee--since thou dost not credit the prophet's words.

sign--a miraculous token to assure thee that God will fulfil His promise of saving Jerusalem (Is 37:30; 38:7, 8). "Signs," facts then present or near at hand as pledges for the more distant future, are frequent in Isaiah.

ask ... in ... depth--literally, "Make deep ... ask it," that is, Go to the depth of the earth or of Hades [Vulgate and Lowth], or, Mount high for it (literally, "Make high"). So in Mt 16:1. Signs in heaven are contrasted with the signs on earth and below it (raising the dead) which Jesus Christ had wrought (compare Ro 10:6, 7). He offers Ahaz the widest limits within which to make his choice.