Gargamuni: Purport. "Vāsudevāya means to Kṛṣṇa, the son of Vasudeva. As by chanting the name of Kṛṣṇa, Vāsudeva, one can achieve all the good results of charity, austerity, and penances, so by the chanting of this mantra, oṁ namo bhagavate vāsudevāya, it is to be understood that the author or the speaker or any one of the readers of Śrīmad-Bhāgavatam offer respectful obeisances unto the Supreme Lord Kṛṣṇa, the reservoir of all pleasure. In the First Canto of Śrīmad-Bhāgavatam, the principles of creation are described, and as such the First Canto can be called 'Creation.' "
Prabhupāda: So this om means addressing the Lord. In the all the Vedic mantras they are addressing. Our this Hare Kṛṣṇa mantra, mahā-mantra, that is also addressing. Hare, Hare, addressing the energy of the Lord, Harā. The energy is Harā, Rādhā, Sītā. So when a female is addressed, it is like that: Hare, Late, Sīte, Rādhe. So Hare means addressing first, first of all the energy. The impersonalists, they do not know this, this addressing first of all Kṛṣṇa's energy. We Gauḍīya Vaiṣṇavas, we don't worship Kṛṣṇa alone, ekala-vāsudeva. No. We must worship Kṛṣṇa along with His energy. Just like Kṛṣṇārjuna, Kṛṣṇa and Arjuna. Arjuna is also energy, living entity, and Kṛṣṇa, Rādhā-Kṛṣṇa, His internal energy, and marginal energy. So Kṛṣṇa means with His energy. Oṁ namo bhagavate vāsudevāya. This bhagavate means full of energies. I have several times explained bhagavān. Bhaga means opulence, and vān means one who possesses. Bhagavān. That is the meaning of word bhagavān. So when this bhagavān word is addressed, it is addressed as bhagavate. The word is bhagavat, bhagavat-śabda. Of course, these are grammatical arrangement. Vat, this affix, is there when it is meant... Sanskrit, every word, every syllable, has got meaning. That is Sanskrit language. It is not like that "beauty but, (?) beauty put." No. If you say "beauty but," then you must say "peauty put." But in English, "beauty but, peauty put." So in Sanskrit language, you cannot do like that. If you have to follow the rules, then the same rule will go on. So bhagavate address, oṁ namo bhagavate vāsudevāya. Vāsudevāya. This is the form of, fourth form of, śabda, sound vibration, fourth form. Just like kṛṣṇāya. When I offer something, kṛṣṇāya, viṣṇave. Similarly, bhagavate, vāsudevāya.