Equality check is DOUBLE equation sign. ==
With only one = you make ySpeed equal to zero so the jump stops immediately.
Also, for jumping up you should decrement yPos instead of incrementing it, since Y coordinates increase from the top of screen towards the bottom. And ySpeed should be decremented always, not only when it's equal to MaxJump, since in that case it will be decremented only once and it will never reach zero. Last, you should include a dbSprite instruction before dbSync, to display your sprite at the new coordinates, otherwise the sprite will never move.
Here is a modified code, summarizing all the above, does that work better?
Fatman.Movement();//Just moving left and right...
if (dbUpKey()==1 && !JumpUp) JumpUp=true;
if (JumpUp) {
yPos -= ySpeed;
dbText(340, 240, \\\"JUMPING!\\\");
ySpeed--;
if (ySpeed==0) JumpUp=false;
}
dbSprite(1,xPos,yPos,1);
if ( dbEscapeKey ( ) ) break;
dbSync ( );