Hi folks.
A decade and a half after I last took a formal piano lesson, I decided to start teaching myself again. I selected a number of pieces I'm interested in learning to play and started learning to play them.
In one of them, however, I'm encountering a difficulty right at the very start:

Two questions about this piece:
1) What is the little hat symbol above the first chord in each bar? It looks like a rest, and at first I thought it was referring to the right hand resting for the first half of each bar before playing that chord. But in the last two bars nobody is resting.
2) How do I play the second left-hand chord in each bar? My left hand is occupied with holding down the first chord. I can play it with my right hand at first, but in the last two bars my right hand is busy doing its own thing.
Thanks much,
Daniel
This is really similar to what everyone else is saying, but at the same time a little different. I hope I don't confuse you.
1) It's kinda hard to describe what that rest means. It's actually very simple, though, once you understand it. In the bass clef, there are two "voices" or "layers" and there is a half rest (minim rest, for those of you not in the US) on the "top" voice. The "layers" in the treble clef are silent. It's kind of like there's an imaginary stave in between the treble and bass clef.
2) I
strongly suggest you play the notes in the "top" voice with the RH, because honestly there is no other way!

Just because something is in the bass clef doesn't mean it
has to be played by the RH; the clefs are only to notate pitch, really. (Of course, that doesn't mean you
shouldn't play things in the bass clef with the left hand, but you don't have to strictly follow that all the time either.)
For the last two bars, though, you can probably use the pedal to "hold" down the whole note like j_menz said. This applies to most pieces in general- when they demand these kinds of things it's ok to use the pedal.