ADVERB (2)

1. with hope; in a hopeful manner;
- Example: "we searched hopefully for a good position"

2. it is hoped;
- Example: "hopefully the weather will be fine on Sunday"

The Collaborative International Dictionary of English v.0.48:

Hopeful \Hope"ful\, a.
   1. Full of hope, or agreeable expectation; inclined to hope;
      expectant.
      [1913 Webster]

            Men of their own natural inclination hopeful and
            strongly conceited.                   --Hooker.
      [1913 Webster]

   2. Having qualities which excite hope; affording promise of
      good or of success; as, a hopeful youth; a hopeful
      prospect. "Hopeful scholars." --Addison. -- Hope"ful*ly,
      adv. -- Hope"ful*ness, n.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Hopefully \Hope"ful*ly\, adv.
   1. In a hopeful manner.
      [PJC]

   2. I hope; if all goes well; as, hopefully, the dress will be
      ready before the party.

   Note: Some prescriptivists object to this usage as being
         ungrammatical, but it is very common and well
         understood. It is usually used to begin a sentence
         describing a desired future event.
         [PJC]

WordNet (r) 3.0 (2006):

hopefully
    adv 1: with hope; in a hopeful manner; "we searched hopefully
           for a good position" [ant: hopelessly]
    2: it is hoped; "hopefully the weather will be fine on Sunday"