1.
I'm sorry to trouble you; excuse me for bothering you
A humble expression used when making a request or causing inconvenience.
恐れ入りますが、もう一度説明していただけますか。
I'm sorry to trouble you, but could you explain that once more?
恐れ入りますが、少々お待ちください。
I'm sorry, but please wait a moment.
恐れ入りますが、こちらにご署名をお願いいたします。
I'm sorry to trouble you, but please sign here.
お忙しいところ恐れ入りますが、確認をお願いできますか。
I know you're busy, but could I ask you to check this?
2.
thank you very much; I'm much obliged
A humble expression of gratitude when someone has done something for you.
わざわざお越しいただき、恐れ入ります。
Thank you so much for taking the trouble to come.
ご配慮いただき、恐れ入ります。
I'm very grateful for your consideration.
お心遣いいただき、恐れ入ります。
I'm truly grateful for your thoughtfulness.
FORMALITY:
This is a very polite/humble expression commonly used in business settings and customer service. The past form 恐れ入りました is also used.
COMMON PATTERNS:
- 恐れ入りますが〜 - I'm sorry to trouble you, but... (preceding a request)
- お忙しいところ恐れ入りますが - I know you're busy, but...
- わざわざ〜恐れ入ります - Thank you for going out of your way to...
RELATED EXPRESSIONS:
- 申し訳ございません - I'm terribly sorry (apologizing for trouble caused)
- 失礼いたします - Excuse me (more general)